메뉴 건너뛰기




Volumn 88, Issue 1-3, 2009, Pages 3-30

On baxter Q-operators and their arithmetic implications

Author keywords

Archimedean L function; Baxter operator; Quantum Toda chain

Indexed keywords


EID: 67349138728     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-008-0285-0     Document Type: Article
Times cited : (6)

References (49)
  • 3
    • 0002561683 scopus 로고
    • Height pairings between algebraic cycles
    • Manin, Yu.I. (ed.) Moscow 1984-86. Lecture Notes in Mathematics Springer, Berlin
    • Beilinson, A.A.: Height pairings between algebraic cycles. In: Manin, Yu.I. (ed.) K-theory, Arithmetic and Geometry, Moscow 1984-86. Lecture Notes in Mathematics, vol. 1289, pp. 1-25. Springer, Berlin (1987).
    • (1987) K-theory, Arithmetic and Geometry , vol.1289 , pp. 1-25
    • Beilinson . A, A.1
  • 4
    • 0003325638 scopus 로고
    • Contemp. Math. 67, 1-24 (1987)
    • (1987) Contemp. Math , vol.67 , pp. 1-24
  • 5
    • 67349170304 scopus 로고    scopus 로고
    • Beilinson, A., Drinfeld, V.: Opers. arXiv:math.AG/0501398
    • Beilinson, A., Drinfeld, V.: Opers. arXiv:math.AG/0501398
  • 6
    • 0032647538 scopus 로고    scopus 로고
    • The Riemann zeros and eigenvalue asymptotics
    • M.V. Berry J.P. Keating 1999 The Riemann zeros and eigenvalue asymptotics SIAM Rev. 41 2 236 266
    • (1999) SIAM Rev. , vol.41 , Issue.2 , pp. 236-266
    • Berry, M.V.1    Keating, J.P.2
  • 8
    • 0001639984 scopus 로고
    • The unramified principal series of p-adic groups II. the Whittaker function
    • W. Casselman J. Shalika 1980 The unramified principal series of p-adic groups II. The Whittaker function Compositio Math. 41 207 231
    • (1980) Compositio Math. , vol.41 , pp. 207-231
    • Casselman, W.1    Shalika, J.2
  • 9
    • 0009938356 scopus 로고
    • Quantum groups as hidden symmetries of classic representation theory
    • Chester, 1988 World Scientific, Teaneck
    • Cherednik, I.V.: Quantum groups as hidden symmetries of classic representation theory. In: Differential Geometric Methods in Theoretical Physics (Chester, 1988), pp. 47-54. World Scientific, Teaneck (1989)
    • (1989) Differential Geometric Methods in Theoretical Physics , pp. 47-54
    • Cherednik, I.V.1
  • 11
    • 53149152987 scopus 로고    scopus 로고
    • Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
    • arXiv:math.NT/9811068
    • A. Connes 1999 Trace formula in noncommutative geometry and the zeros of the Riemann zeta function Sel. Math. (NS) 5 29 106 arXiv:math.NT/9811068
    • (1999) Sel. Math. (NS) , vol.5 , pp. 29-106
    • Connes, A.1
  • 13
    • 0000299430 scopus 로고
    • On the Γ-factors attached to motives
    • C. Deninger 1991 On the Γ-factors attached to motives Invent. Math. 104 245 261
    • (1991) Invent. Math. , vol.104 , pp. 245-261
    • Deninger, C.1
  • 14
    • 0040652366 scopus 로고
    • Local L-factors of motives and regularized determinants
    • C. Deninger 1992 Local L-factors of motives and regularized determinants Invent. Math. 107 135 150
    • (1992) Invent. Math. , vol.107 , pp. 135-150
    • Deninger, C.1
  • 15
    • 0033600680 scopus 로고    scopus 로고
    • Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations
    • arXiv:hep-th/9812211
    • P. Dorey R. Tateo 1999 Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations J. Phys. A 32 L419 L425 arXiv:hep-th/9812211
    • (1999) J. Phys. A , vol.32
    • Dorey, P.1    Tateo, R.2
  • 16
    • 0033590228 scopus 로고    scopus 로고
    • on the relation between Stokes multipliers and T-Q systems of conformal field theory
    • (30). arXiv:hep-th/9906219
    • Dorey, P., Tateo, R.: On the relation between Stokes multipliers and T-Q systems of conformal field theory. Nucl. Phys. B 563(3), 573-602(30). arXiv:hep-th/9906219
    • Nucl. Phys. B , vol.563 , Issue.3 , pp. 573-602
    • Dorey, P.1    Tateo, R.2
  • 17
    • 0002189545 scopus 로고    scopus 로고
    • Whittaker functions on quantum groups and q-deformed Toda operators
    • American Mathematical Society, Providence arXiv:math.QA/9901053
    • Etingof, P.: Whittaker functions on quantum groups and q-deformed Toda operators. Am. Math. Soc. Transl. Ser. 2, vol. 194, pp. 9-25. American Mathematical Society, Providence (1999). arXiv:math.QA/9901053
    • (1999) Am. Math. Soc. Transl. ser , vol.194 , Issue.2 , pp. 9-25
    • Etingof, P.1
  • 18
    • 0001817663 scopus 로고
    • Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras
    • Tsuchiya, A., Eguchi, T., Jimbo, M. (eds.) World Scientific, Singapore
    • Feigin, B., Frenkel, E.: Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras. In: Tsuchiya, A., Eguchi, T., Jimbo, M. (eds.) Infinite Analysis. Adv. Ser. in Math. Phys., vol. 16, pp. 197-215. World Scientific, Singapore (1992)
    • (1992) Infinite Analysis. Adv. Ser. in Math. Phys , vol.16 , pp. 197-215
    • Feigin, B.1    Frenkel, E.2
  • 19
    • 0003386464 scopus 로고
    • Affine algebras, Langlands duality and Bethe ansatz
    • Iagolnitzer, D. (ed.) Paris International Press, New York (1995). arXiv:math.QA/9506003
    • Frenkel, E.: Affine algebras, Langlands duality and Bethe ansatz. In: Iagolnitzer, D. (ed.) Proceedings of the International Congress of Mathematical Physics, Paris, 1994, pp. 606-642. International Press, New York (1995). arXiv:math.QA/9506003
    • (1994) Proceedings of the International Congress of Mathematical Physics , pp. 606-642
    • Frenkel, E.1
  • 20
    • 1842683028 scopus 로고    scopus 로고
    • Representation Theory and Quantum Inverse Scattering Method: The Open Toda Chain and the Hyperbolic Sutherland Model
    • A. Gerasimov S. Kharchev D. Lebedev 2004 Representation theory and quantum inverse scattering method: open Toda chain and hyperbolic Sutherland model Int. Math. Res. Notes 17 823 854 arXiv:math.QA/0204206 (Pubitemid 38483028)
    • (2004) International Mathematics Research Notices , Issue.17 , pp. 823-854
    • Gerasimov, A.1    Kharchev, S.2    Lebedev, D.3
  • 21
    • 55149083730 scopus 로고    scopus 로고
    • Baxter operator and Archimedean Hecke algebra
    • doi: 10.1007/s00220-008-0547-9.arXiv:math.RT/0706.347
    • Gerasimov, A., Lebedev, D., Oblezin, S.: Baxter operator and Archimedean Hecke algebra. Commun. Math. Phys. doi: 10.1007/s00220-008-0547-9. arXiv:math.RT/0706. 347
    • Commun. Math. Phys.
    • Gerasimov, A.1    Lebedev, D.2    Oblezin, S.3
  • 23
    • 21844486554 scopus 로고    scopus 로고
    • Quantum cohomology of flag manifolds and Toda lattices
    • arXiv.org:hep-th/9312096
    • Givental, A., Kim, B.: Quantum cohomology of flag manifolds and Toda lattices. Commun. Math. Phys. 168, 609. arXiv.org:hep-th/9312096
    • Commun. Math. Phys. , vol.168 , pp. 609
    • Givental, A.1    Kim, B.2
  • 24
    • 0009242617 scopus 로고    scopus 로고
    • Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture
    • Topics in Singularity Theory American Mathematical Society, Providence arXiv:alg-geom/9612001
    • Givental, A.: Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture. Topics in Singularity Theory. American Mathematical Society Transl. Ser., 2, vol. 180, pp. 103-115. American Mathematical Society, Providence (1997). arXiv:alg-geom/9612001
    • (1997) American Mathematical Society Transl. Ser. , vol.180 , Issue.2 , pp. 103-115
    • Givental, A.1
  • 25
    • 0037214431 scopus 로고    scopus 로고
    • Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups
    • arXiv:math/0108105
    • A. Givental Y.-P. Lee 2003 Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups Invent. Math. 151 193 219 arXiv:math/0108105
    • (2003) Invent. Math. , vol.151 , pp. 193-219
    • Givental, A.1    Lee, Y.-P.2
  • 26
    • 0001268228 scopus 로고
    • The quantum mechanical Toda lattice II
    • M. Gutzwiller 1981 The quantum mechanical Toda lattice II Ann. Phys. 133 304 331
    • (1981) Ann. Phys. , vol.133 , pp. 304-331
    • Gutzwiller, M.1
  • 28
    • 0035626477 scopus 로고    scopus 로고
    • Double affine Hecke algebras and 2-dimensional local fields
    • arXiv:math.AG/9812021
    • M. Kapranov 2001 Double affine Hecke algebras and 2-dimensional local fields J. AMS 14 239 262 arXiv:math.AG/9812021
    • (2001) J. AMS , vol.14 , pp. 239-262
    • Kapranov, M.1
  • 29
    • 0038530105 scopus 로고    scopus 로고
    • Harmonic analysis on algebraic groups over two-dimensional local fields of equal characteristic
    • Invitation to Higher Local Fields Part II Sect. 5
    • Kapranov, M.: Harmonic analysis on algebraic groups over two-dimensional local fields of equal characteristic. In: Geometry and Topology Monographs. Invitation to Higher Local Fields Part II, vol. 3, Sect. 5, pp. 255-262
    • Geometry and Topology Monographs , vol.3 , pp. 255-262
    • Kapranov, M.1
  • 30
    • 0041036533 scopus 로고    scopus 로고
    • Eigenfunctions of GL(N, R) Toda chain: The Mellin-Barnes representation
    • arXiv:hep-th/0004065
    • S. Kharchev D. Lebedev 2000 Eigenfunctions of GL(N, R) Toda chain: the Mellin-Barnes representation JETP Lett. 71 235 238 arXiv:hep-th/0004065
    • (2000) JETP Lett. , vol.71 , pp. 235-238
    • Kharchev, S.1    Lebedev, D.2
  • 31
    • 0035937681 scopus 로고    scopus 로고
    • Integral representations for the eigenfunctions of quantum open and periodic Toda chains from QISM formalism
    • S. Kharchev D. Lebedev 2001 Integral representations for the eigenfunctions of quantum open and periodic Toda chains from QISM formalism J. Phys. A34 2247 2258
    • (2001) J. Phys. , vol.34 , pp. 2247-2258
    • Kharchev, S.1    Lebedev, D.2
  • 32
    • 2442630408 scopus 로고    scopus 로고
    • Unitary representations of Uq(S-fraktur signl}(2,ℝ)), the modular double and the multiparticle q-deformed toda chain
    • DOI 10.1007/s002200100592
    • q (sl(2, R)), the modular double and the multiparticle q-deformed Toda chains. Commun Math. Phys. 225 3 573 609 arXiv:hep-th/0102180 (Pubitemid 40849803)
    • (2002) Communications in Mathematical Physics , vol.225 , Issue.3 , pp. 573-609
    • Kharchev, S.1    Lebedev, D.2    Semenov-Tian-Shansky, M.3
  • 34
    • 0001043985 scopus 로고
    • Quantization and representation theory
    • Represenatation Theory of Lie Groups London Mathematical Society, Oxford
    • Kostant, B.: Quantization and representation theory. In: Represenatation Theory of Lie Groups. Lecture Notes Series, vol. 34, pp. 287-316. London Mathematical Society, Oxford (1979)
    • (1979) Lecture Notes Series , vol.34 , pp. 287-316
    • Kostant, B.1
  • 35
    • 0000482115 scopus 로고
    • On Whittaker vectors and representation theory
    • B. Kostant 1978 On Whittaker vectors and representation theory Invent. Math. 48 2 101 184
    • (1978) Invent. Math. , vol.48 , Issue.2 , pp. 101-184
    • Kostant, B.1
  • 37
    • 33646429206 scopus 로고    scopus 로고
    • The notion of dimension in geometry and algebra
    • arXiv:math/0502016
    • Yu.I. Manin 2006 The notion of dimension in geometry and algebra Bull. AMS (NS) 43 2 139 161 arXiv:math/0502016
    • (2006) Bull. AMS (NS) , vol.43 , Issue.2 , pp. 139-161
    • Manin, Yu.I.1
  • 39
    • 0011544175 scopus 로고
    • On the arithmetic of 2-dimensional schemes. i Repartitions and residues
    • A.N. Parshin 1976 On the arithmetic of 2-dimensional schemes. I Repartitions and residues Russ. Math. Izv. 40 736 773
    • (1976) Russ. Math. Izv. , vol.40 , pp. 736-773
    • Parshin, A.N.1
  • 40
    • 33645677331 scopus 로고
    • The periodic Toda chain and a matrix generalization of the Bessel function recursion relation
    • V. Pasquier M. Gaudin 1992 The periodic Toda chain and a matrix generalization of the Bessel function recursion relation J. Phys. A 25 5243 5252
    • (1992) J. Phys. A , vol.25 , pp. 5243-5252
    • Pasquier, V.1    Gaudin, M.2
  • 41
    • 0000710748 scopus 로고
    • The relativistic Toda systems
    • S. Ruijsenaars 1990 The relativistic Toda systems Commun. Math. Phys. 133 217 247
    • (1990) Commun. Math. Phys. , vol.133 , pp. 217-247
    • Ruijsenaars, S.1
  • 44
    • 0000315646 scopus 로고
    • The quantum Toda chain
    • E. Sklyanin 1985 The quantum Toda chain Lect. Notes Phys. 226 196 233
    • (1985) Lect. Notes Phys. , vol.226 , pp. 196-233
    • Sklyanin, E.1
  • 45
    • 0142199784 scopus 로고    scopus 로고
    • Archimedean L-functions and Barnes integrals
    • E. Stade 2002 Archimedean L-functions and Barnes integrals Isr. J. Math. 127 201 219
    • (2002) Isr. J. Math. , vol.127 , pp. 201-219
    • Stade, E.1
  • 46
    • 0000523006 scopus 로고
    • Number theoretic background
    • Automorphic forms and L-functions part 2
    • Tate, J.: Number theoretic background. In: Automorphic forms and L-functions. Proceedings of Symposia in Pure Mathematics, vol. 33, part 2, pp. 3-26 (1979)
    • (1979) Proceedings of Symposia in Pure Mathematics , vol.33 , pp. 3-26
    • Tate, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.