메뉴 건너뛰기




Volumn 197, Issue , 2010, Pages 59-174

Periodicities of T-systems and Y-systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77956141183     PISSN: 00277630     EISSN: None     Source Type: Journal    
DOI: 10.1215/00277630-2009-003     Document Type: Article
Times cited : (52)

References (71)
  • 2
    • 0021422438 scopus 로고
    • Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
    • G. E. Andrews, R. J. Baxter, and P. J. Forrester, Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities, J. Stat. Phys., 35 (1984), 193-266.
    • (1984) J. Stat. Phys. , vol.35 , pp. 193-266
    • Andrews, G.E.1    Baxter, R.J.2
  • 3
    • 33947305366 scopus 로고    scopus 로고
    • Elements of the Representation Theory of Associative Algebras, Vol. 1, Techniques of Representation Theory
    • Cambridge University Press, Cambridge
    • I. Assem, D. Simson, and A. Skowronski, Elements of the Representation Theory of Associative Algebras, Vol. 1, Techniques of Representation Theory, London Math. Soc. Stud. Texts 65, Cambridge University Press, Cambridge, 2006.
    • (2006) London Math. Soc. Stud. Texts , vol.65
    • Assem, I.1    Simson, D.2    Skowronski, A.3
  • 4
    • 0003310131 scopus 로고
    • Representation Theory of Artin Algebras
    • Cambridge University Press, Cambridge
    • M. Auslander, I. Reiten, and S. O. Smalo, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge University Press, Cambridge, 1995.
    • (1995) Cambridge Stud. Adv. Math , vol.36
    • Auslander, M.1    Reiten, I.2    Smalo, S.O.3
  • 5
    • 0000798070 scopus 로고
    • Restricted solid-on-solid models connected with simply laced algebras and conformal field theory
    • V. V. Bazhanov and N. Reshetikhin, Restricted solid-on-solid models connected with simply laced algebras and conformal field theory, J. Phys. A, 23 (1990), 1477-1492.
    • (1990) J. Phys. A , vol.23 , pp. 1477-1492
    • Bazhanov, V.V.1    Reshetikhin, N.2
  • 7
    • 85037209375 scopus 로고    scopus 로고
    • Cluster structures for 2-Calabi-Yau categories and unipotent groups
    • to appear in, preprint, arXiv:math/0701557
    • A. Buan, O. Iyama, I. Reiten, and J. Scott, Cluster structures for 2-Calabi-Yau categories and unipotent groups, to appear in Compos. Math., preprint, arXiv:math/0701557.
    • Compos. Math.
    • Buan, A.1    Iyama, O.2    Reiten, I.3    Scott, J.4
  • 8
    • 39749119984 scopus 로고    scopus 로고
    • Cluster mutation via quiver representations
    • A. Buan, R. Marsh, and I. Reiten, Cluster mutation via quiver representations, Comment. Math. Helv., 83 (2008), 143-177.
    • (2008) Comment. Math. Helv. , vol.83 , pp. 143-177
    • Buan, A.1    Marsh, R.2    Reiten, I.3
  • 10
    • 33750855116 scopus 로고    scopus 로고
    • Cluster algebras as Hall algebras of quiver representations
    • P. Caldero and F. Chapoton, Cluster algebras as Hall algebras of quiver representations, Comment. Math. Helv., 81 (2006), 595-616.
    • (2006) Comment. Math. Helv. , vol.81 , pp. 595-616
    • Caldero, P.1    Chapoton, F.2
  • 11
    • 0037850480 scopus 로고    scopus 로고
    • A topological invariant of RG flows in 2D integrable quantum field theories
    • R. Caracciolo, F. Gliozzi, and R. Tateo, A topological invariant of RG flows in 2D integrable quantum field theories, Int. J. Mod. Phys., 13 (1999), 2927-2932.
    • (1999) Int. J. Mod. Phys , vol.13 , pp. 2927-2932
    • Caracciolo, R.1    Gliozzi, F.2    Tateo, R.3
  • 12
    • 41249083675 scopus 로고    scopus 로고
    • From triangulated categories to cluster algebras
    • P. Caldero and B. Keller, From triangulated categories to cluster algebras, Invent. Math., 172 (2008), 169-211.
    • (2008) Invent. Math. , vol.172 , pp. 169-211
    • Caldero, P.1    Keller, B.2
  • 13
    • 33947407721 scopus 로고    scopus 로고
    • From triangulated categories to cluster algebras, II
    • P. Caldero and B. Keller, From triangulated categories to cluster algebras, II, Ann. Sci. Ecole Norm. Sup., 39 (2006), 983-1009.
    • (2006) Ann. Sci. Ecole Norm. Sup. , vol.39 , pp. 983-1009
    • Caldero, P.1    Keller, B.2
  • 14
    • 0007109637 scopus 로고
    • Quantum affine algebras
    • V. Chari and A. Pressley, Quantum affine algebras, Comm. Math. Phys., 142 (1991), 261-283.
    • (1991) Comm. Math. Phys , vol.142 , pp. 261-283
    • Chari, V.1    Pressley, A.2
  • 15
    • 0002978237 scopus 로고
    • Quantum affine algebras and their representations
    • Banff, 1994, CMS Conf. Proc. 16
    • V. Chari and A. Pressley, Quantum affine algebras and their representations, in Proceedings of Representations of Groups, Banff, 1994, 59-78, CMS Conf. Proc. 16, 1995.
    • (1995) Proceedings of Representations of Groups , pp. 59-78
    • Chari, V.1    Pressley, A.2
  • 16
    • 61749087162 scopus 로고    scopus 로고
    • On the combinatorics of rigid objects in 2-Calabi-Yau categories
    • rnn029
    • R. Dehy and B. Keller, On the combinatorics of rigid objects in 2-Calabi-Yau categories, Int. Math. Res. Not. IMRN, 2008 (2008) rnn029, 17 pages.
    • (2008) Int. Math. Res. Not. IMRN , Issue.2008 , pp. 17
    • Dehy, R.1    Keller, B.2
  • 18
    • 0000911818 scopus 로고
    • Hopf algebras and the quantum Yang-Baxter equation
    • V. Drinfel’d, Hopf algebras and the quantum Yang-Baxter equation, Soviet. Math. Dokl., 32 (1985), 254-258.
    • (1985) Soviet. Math. Dokl. , vol.32 , pp. 254-258
    • Drinfel’d, V.1
  • 19
    • 0000503475 scopus 로고
    • A new realization of Yangians and quantized affine algebras
    • V. Drinfel’d, A new realization of Yangians and quantized affine algebras, Soviet Math. Dokl., 36 (1988), 212-216.
    • (1988) Soviet Math. Dokl. , vol.36 , pp. 212-216
    • Drinfel’d, V.1
  • 20
    • 0036004369 scopus 로고    scopus 로고
    • Cluster algebras I, Foundations
    • S. Fomin and A. Zelevinsky, Cluster algebras I, Foundations, J. Amer. Math. Soc., 15 (2002), 497-529.
    • (2002) J. Amer. Math. Soc. , vol.15 , pp. 497-529
    • Fomin, S.1    Zelevinsky, A.2
  • 21
    • 0141457388 scopus 로고    scopus 로고
    • Cluster algebras II, Finite type classification
    • S. Fomin and A. Zelevinsky, Cluster algebras II, Finite type classification, Invent. Math., 154 (2003), 63-121.
    • (2003) Invent. Math. , vol.154 , pp. 63-121
    • Fomin, S.1    Zelevinsky, A.2
  • 22
    • 0347188734 scopus 로고    scopus 로고
    • Y-systems and generalized associahedra
    • S. Fomin and A. Zelevinsky, Y-systems and generalized associahedra, Ann. of Math., 158 (2003), 977-1018.
    • (2003) Ann. Of Math. , vol.158 , pp. 977-1018
    • Fomin, S.1    Zelevinsky, A.2
  • 23
    • 34248372052 scopus 로고    scopus 로고
    • Cluster algebras IV, Coefficients
    • S. Fomin and A. Zelevinsky, Cluster algebras IV, Coefficients, Compos. Math., 143 (2007), 112-164.
    • (2007) Compos. Math. , vol.143 , pp. 112-164
    • Fomin, S.1    Zelevinsky, A.2
  • 24
    • 0035530560 scopus 로고    scopus 로고
    • Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras
    • E. Frenkel and E. Mukhin, Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras, Comm. Math. Phys., 216 (2001), 23-57.
    • (2001) Comm. Math. Phys. , vol.216 , pp. 23-57
    • Frenkel, E.1    Mukhin, E.2
  • 25
    • 0037109523 scopus 로고    scopus 로고
    • The q-characters at roots of unity
    • E. Frenkel and E. Mukhin, The q-characters at roots of unity, Adv. Math., 171 (2002), 139-167.
    • (2002) Adv. Math. , vol.171 , pp. 139-167
    • Frenkel, E.1    Mukhin, E.2
  • 26
    • 0000268226 scopus 로고    scopus 로고
    • The q-characters of representations of quantum affine algebras and deformations of W-algebras
    • E. Frenkel and N. Reshetikhin, The q-characters of representations of quantum affine algebras and deformations of W-algebras, Contemp. Math., 248 (1999), 163-205.
    • (1999) Contemp. Math. , vol.248 , pp. 163-205
    • Frenkel, E.1    Reshetikhin, N.2
  • 27
    • 21844522302 scopus 로고
    • Thermodynamic Bethe ansatz and dilogarithm identities, I
    • E. Frenkel and A. Szenes, Thermodynamic Bethe ansatz and dilogarithm identities, I, Math. Res. Lett., 2 (1995), 677-693.
    • (1995) Math. Res. Lett. , vol.2 , pp. 677-693
    • Frenkel, E.1    Szenes, A.2
  • 29
    • 0000412896 scopus 로고    scopus 로고
    • Thermodynamic Bethe ansatz and three-fold triangulations
    • F. Gliozzi and R. Tateo, Thermodynamic Bethe ansatz and three-fold triangulations, Int. J. Mod. Phys. A, 11 (1996), 4051-4064.
    • (1996) Int. J. Mod. Phys. A , vol.11 , pp. 4051-4064
    • Gliozzi, F.1    Tateo, R.2
  • 30
    • 0003275895 scopus 로고
    • Triangulated Categories in the Representation Theory of FiniteDimensional Algebras
    • Cambridge University Press, Cambridge
    • D. Happel, Triangulated Categories in the Representation Theory of FiniteDimensional Algebras, London Math. Soc. Lecture Note Ser. 119, Cambridge University Press, Cambridge, 1988.
    • (1988) London Math. Soc. Lecture Note Ser , vol.119
    • Happel, D.1
  • 31
  • 33
    • 34547700546 scopus 로고    scopus 로고
    • A periodicity theorem for the octahedron recurrence
    • A. Henriques, A periodicity theorem for the octahedron recurrence, J. Algebraic Combin., 26 (2007), 1-26.
    • (2007) J. Algebraic Combin. , vol.26 , pp. 1-26
    • Henriques, A.1
  • 34
    • 33747360376 scopus 로고    scopus 로고
    • The Kirillov-Reshetikhin conjecture and solutions of T-systems
    • D. Hernandez, The Kirillov-Reshetikhin conjecture and solutions of T-systems, J. Reine Angew. Math., 596 (2006), 63-87.
    • (2006) J. Reine Angew. Math. , vol.596 , pp. 63-87
    • Hernandez, D.1
  • 36
    • 85037227248 scopus 로고    scopus 로고
    • preparation; and talk presented by B. Leclerc at Workshop “Lie Theory” held at MSRI, Berkeley, March
    • D. Hernandez and B. Leclerc, Cluster algebras and quantum affine algebras, in preparation; and talk presented by B. Leclerc at Workshop “Lie Theory” held at MSRI, Berkeley, March 2008.
    • (2008) Cluster Algebras and Quantum Affine Algebras
    • Hernandez, D.1    Leclerc, B.2
  • 37
    • 11744280164 scopus 로고
    • Nonlinear partial difference equations II: Discrete time Toda equations
    • R. Hirota, Nonlinear partial difference equations II: Discrete time Toda equations, J. Phys. Soc. Japan, 43 (1977), 2074-2078.
    • (1977) J. Phys. Soc. Japan , vol.43 , pp. 2074-2078
    • Hirota, R.1
  • 38
    • 0000090564 scopus 로고
    • Discrete two-dimensional Toda molecule equation
    • R. Hirota, Discrete two-dimensional Toda molecule equation, J. Phys. Soc. Japan, 56 (1987), 4285-4288.
    • (1987) J. Phys. Soc. Japan , vol.56 , pp. 4285-4288
    • Hirota, R.1
  • 39
    • 41149141379 scopus 로고    scopus 로고
    • Mutation in triangulated categories and, rigid Cohen-Macaulay modules
    • O. Iyama and Y. Yoshino, Mutation in triangulated categories and, rigid Cohen-Macaulay modules, Invent. Math., 172 (2008), 117-168.
    • (2008) Invent. Math. , vol.172 , pp. 117-168
    • Iyama, O.1    Yoshino, Y.2
  • 40
    • 0040323775 scopus 로고
    • A q-difference analogue of U(@) and, the Yang-Baxter equation
    • M. Jimbo, A q-difference analogue of U(@) and, the Yang-Baxter equation, Lett. Math. Phys., 10 (1985), 63-69.
    • (1985) Lett. Math. Phys. , vol.10 , pp. 63-69
    • Jimbo, M.1
  • 41
    • 0001370587 scopus 로고
    • Solvable lattice models related to the vector representation of classical simple Lie algebras
    • M. Jimbo, T. Miwa, and M. Okado, Solvable lattice models related to the vector representation of classical simple Lie algebras, Comm. Math. Phys., 116 (1988), 507-525.
    • (1988) Comm. Math. Phys. , vol.116 , pp. 507-525
    • Jimbo, M.1    Miwa, T.2    Okado, M.3
  • 44
    • 85166329447 scopus 로고    scopus 로고
    • On triangulated orbit categories
    • B. Keller, On triangulated orbit categories, Doc. Math., 10 (2005), 551-581.
    • (2005) Doc. Math. , vol.10 , pp. 551-581
    • Keller, B.1
  • 48
    • 0001438677 scopus 로고
    • Identities for the Rogers dilogarithm function connected with simple Lie algebras
    • A. N. Kirillov, Identities for the Rogers dilogarithm function connected with simple Lie algebras, J. Sov. Math., 47 (1989), 2450-2459.
    • (1989) J. Sov. Math. , vol.47 , pp. 2450-2459
    • Kirillov, A.N.1
  • 50
    • 34249954468 scopus 로고
    • Representations of Yangians and multiplicities of the inclusion of the irreducible components of the tensor product of representations of simple Lie algebras
    • A. N. Kirillov and N. Reshetikhin, Representations of Yangians and multiplicities of the inclusion of the irreducible components of the tensor product of representations of simple Lie algebras, J. Sov. Math., 52 (1990), 3156-3164.
    • (1990) J. Sov. Math. , vol.52 , pp. 3156-3164
    • Kirillov, A.N.1    Reshetikhin, N.2
  • 51
    • 33751275929 scopus 로고
    • Conformal weights of RSOS lattice models and, their fusion hierarchies
    • A. Klumper and P. A. Pearce, Conformal weights of RSOS lattice models and, their fusion hierarchies, Phys. A, 183 (1992), 304-350.
    • (1992) Phys. A , vol.183 , pp. 304-350
    • Klumper, A.1    Pearce, P.A.2
  • 52
    • 0000487016 scopus 로고
    • Spectra of tensor products of finite-dimensional representations of Yangians
    • H. Knight, Spectra of tensor products of finite-dimensional representations of Yangians, J. Algebra, 174 (1995), 187-196.
    • (1995) J. Algebra , vol.174 , pp. 187-196
    • Knight, H.1
  • 53
    • 0041048843 scopus 로고    scopus 로고
    • Quantum integrable models and discrete classical Hirota equations
    • I. Krichever, O. Lipan, P. Wiegmann, and A. Zabrodin, Quantum integrable models and discrete classical Hirota equations, Comm. Math. Phys., 188 (1997), 267-304.
    • (1997) Comm. Math. Phys. , vol.188 , pp. 267-304
    • Krichever, I.1    Lipan, O.2    Wiegmann, P.3    Zabrodin, A.4
  • 54
    • 0001558664 scopus 로고
    • Thermodynamics of the Uq(X^1^) Bethe ansatz system with q a root of unity
    • 1^) Bethe ansatz system with q a root of unity, Nucl. Phys. B, 389 (1993), 209-244.
    • (1993) Nucl. Phys. B , vol.389 , pp. 209-244
    • Kuniba, A.1
  • 55
    • 0001144405 scopus 로고
    • Spectra in conformal field theories from the Rogers dilogarithm
    • A. Kuniba and T. Nakanishi, Spectra in conformal field theories from the Rogers dilogarithm, Mod. Phys. Lett. A, 7 (1992), 3487-3494.
    • (1992) Mod. Phys. Lett. A , vol.7 , pp. 3487-3494
    • Kuniba, A.1    Nakanishi, T.2
  • 56
    • 0001663460 scopus 로고
    • Functional relations in solvable lattice models: I. Functional relations and representation theory
    • A. Kuniba, T. Nakanishi, and J. Suzuki, Functional relations in solvable lattice models: I. Functional relations and representation theory, Int. J. Mod. Phys. A, 9 (1994), 5215-5266.
    • (1994) Int. J. Mod. Phys. A , vol.9 , pp. 5215-5266
    • Kuniba, A.1    Nakanishi, T.2    Suzuki, J.3
  • 57
    • 0001663460 scopus 로고
    • Functional relations in solvable lattice models: II. Applications
    • A. Kuniba, T. Nakanishi, and J. Suzuki, Functional relations in solvable lattice models: II. Applications, Int. J. Mod. Phys. A, 9 (1994), 5267-5312.
    • (1994) Int. J. Mod. Phys. A , vol.9 , pp. 5267-5312
    • Kuniba, A.1    Nakanishi, T.2    Suzuki, J.3
  • 58
    • 0036014161 scopus 로고    scopus 로고
    • The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture
    • A. Kuniba, T. Nakanishi, and Z. Tsuboi, The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture, Comm. Math. Phys., 227 (2002), 155-190.
    • (2002) Comm. Math. Phys. , vol.227 , pp. 155-190
    • Kuniba, A.1    Nakanishi, T.2    Tsuboi, Z.3
  • 59
    • 21844515348 scopus 로고
    • Quantum Jacobi-Trudi and Giambelli formulae for Uq(B(1)) from the analytic Bethe ansatz
    • (1)) from the analytic Bethe ansatz, J. Phys. A, 28 (1995), 6211-6226.
    • (1995) J. Phys. A , vol.28 , pp. 6211-6226
    • Kuniba, A.1    Ohta, Y.2    Suzuki, J.3
  • 60
    • 0037085132 scopus 로고    scopus 로고
    • Difference L operators related to q-characters
    • A. Kuniba, M. Okado, J. Suzuki, and Y. Yamada, Difference L operators related to q-characters, J. Phys. A, 35 (2002), 1415-1435.
    • (2002) J. Phys. A , vol.35 , pp. 1415-1435
    • Kuniba, A.1    Okado, M.2    Suzuki, J.3    Yamada, Y.4
  • 61
    • 21844492118 scopus 로고
    • Functional relations and analytic Bethe ansatz for twisted quantum affine algebras
    • A. Kuniba and J. Suzuki, Functional relations and analytic Bethe ansatz for twisted quantum affine algebras, J. Phys. A, 28 (1995), 711-722.
    • (1995) J. Phys. A , vol.28 , pp. 711-722
    • Kuniba, A.1    Suzuki, J.2
  • 62
    • 0035626524 scopus 로고    scopus 로고
    • Quiver varieties and finite dimensional representations of quantum affine algebras
    • H. Nakajima, Quiver varieties and finite dimensional representations of quantum affine algebras, J. Amer. Math. Soc., 14 (2001), 145-238.
    • (2001) J. Amer. Math. Soc. , vol.14 , pp. 145-238
    • Nakajima, H.1
  • 63
    • 21644433869 scopus 로고    scopus 로고
    • Quiver varieties and t-analogues of q-characters of quantum affine algebras
    • H. Nakajima, Quiver varieties and t-analogues of q-characters of quantum affine algebras, Ann. of Math., 160 (2004), 1057-1097.
    • (2004) Ann. Of Math. , vol.160 , pp. 1057-1097
    • Nakajima, H.1
  • 64
    • 18444417390 scopus 로고    scopus 로고
    • T-Analogs of q-characters of Kirillov-Reshetikhin modules of quantum affine algebras, Represent
    • H. Nakajima, t-Analogs of q-characters of Kirillov-Reshetikhin modules of quantum affine algebras, Represent. Theory, 7 (2003), 259-274.
    • (2003) Theory , vol.7 , pp. 259-274
    • Nakajima, H.1
  • 65
    • 57049177105 scopus 로고    scopus 로고
    • Cluster characters for triangulated 2-Calabi-Yau categories
    • Y. Palu, Cluster characters for triangulated 2-Calabi-Yau categories, Ann. Inst. Fourier (Grenoble), 58 (2008), 2221-2248.
    • (2008) Ann. Inst. Fourier (Grenoble) , vol.58 , pp. 2221-2248
    • Palu, Y.1
  • 66
    • 0002375064 scopus 로고    scopus 로고
    • Etiology of IRF models
    • V. Pasquier, Etiology of IRF models, Comm. Math. Phys., 118 (1988), 335-364.
    • Comm. Math. Phys. , vol.118 , Issue.1988 , pp. 335-364
    • Pasquier, V.1
  • 68
    • 0001841091 scopus 로고
    • Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds
    • M. Sato, Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds, RIMS Kokyuroku Bessatsu, 439 (1981), 30-46.
    • (1981) RIMS Kokyuroku Bessatsu , vol.439 , pp. 30-46
    • Sato, M.1
  • 69
    • 35348896597 scopus 로고    scopus 로고
    • On the periodicity conjecture for Y-systems
    • A. Y. Volkov, On the periodicity conjecture for Y-systems, Comm. Math. Phys., 276 (2007), 509-517.
    • (2007) Comm. Math. Phys. , vol.276 , pp. 509-517
    • Volkov, A.Y.1
  • 71
    • 0010071731 scopus 로고
    • On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories
    • Al. B. Zamolodchikov, On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories, Phys. Lett. B, 253 (1991), 391-394.
    • (1991) Phys. Lett. B , vol.253 , pp. 391-394
    • Zamolodchikov, A.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.