메뉴 건너뛰기




Volumn 606, Issue 3, 2001, Pages 547-582

Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials

Author keywords

03.65.Fd; 11.10.Lm; 11.30.Pb; Calogero Moser Sutherland model; Dunkl operators; Jack polynomials; Lax formalism; Supersymmetry

Indexed keywords


EID: 0000544515     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(01)00208-5     Document Type: Article
Times cited : (62)

References (71)
  • 1
    • 0000285630 scopus 로고
    • Ground state of one-dimensional N body system
    • Calogero F. Ground state of one-dimensional N body system. J. Math. Phys. 10:1969;2197.
    • (1969) J. Math. Phys. , vol.10 , pp. 2197
    • Calogero, F.1
  • 2
    • 0000680872 scopus 로고
    • Solution of a three body problem in one dimension
    • Calogero F. Solution of a three body problem in one dimension. J. Math. Phys. 10:1969;2191.
    • (1969) J. Math. Phys. , vol.10 , pp. 2191
    • Calogero, F.1
  • 3
    • 29744455506 scopus 로고
    • Solution of the one-dimensional N body problems with quadratic and/or inversely quadratic pair potentials
    • Calogero F. Solution of the one-dimensional N body problems with quadratic and/or inversely quadratic pair potentials. J. Math. Phys. 12:1971;419.
    • (1971) J. Math. Phys. , vol.12 , pp. 419
    • Calogero, F.1
  • 4
    • 34347230069 scopus 로고
    • Three integrable Hamiltonian systems connected with isospectral deformations
    • Moser J. Three integrable Hamiltonian systems connected with isospectral deformations. Adv. Math. 16:1975;197.
    • (1975) Adv. Math. , vol.16 , pp. 197
    • Moser, J.1
  • 5
    • 0000612877 scopus 로고
    • Quantum many body problem in one dimension: Ground state
    • Sutherland B. Quantum many body problem in one dimension: ground state. J. Math. Phys. 12:1971;246.
    • (1971) J. Math. Phys. , vol.12 , pp. 246
    • Sutherland, B.1
  • 6
    • 24844447275 scopus 로고
    • Exact results for a quantum many body problem in one dimension
    • Sutherland B. Exact results for a quantum many body problem in one dimension. Phys. Rev. A. 4:1971;2019.
    • (1971) Phys. Rev. a , vol.4 , pp. 2019
    • Sutherland, B.1
  • 7
    • 33646946362 scopus 로고
    • Exact results for a quantum many body problem in one dimension II
    • Sutherland B. Exact results for a quantum many body problem in one dimension II. Phys. Rev. A. 5:1972;1372.
    • (1972) Phys. Rev. a , vol.5 , pp. 1372
    • Sutherland, B.1
  • 8
    • 0011546968 scopus 로고
    • Classical integrable finite dimensional systems related to Lie algebras
    • Olshanetsky M.A., Perelomov A.M. Classical integrable finite dimensional systems related to Lie algebras. Phys. Rep. 71:1981;313.
    • (1981) Phys. Rep. , vol.71 , pp. 313
    • Olshanetsky, M.A.1    Perelomov, A.M.2
  • 9
    • 0007456353 scopus 로고
    • Quantum integrable systems related to Lie algebras
    • Olshanetsky M.A., Perelomov A.M. Quantum integrable systems related to Lie algebras. Phys. Rep. 94:1983;313.
    • (1983) Phys. Rep. , vol.94 , pp. 313
    • Olshanetsky, M.A.1    Perelomov, A.M.2
  • 10
    • 84911743709 scopus 로고
    • Rational and elliptic solutions of the Korteweg - De Vries equation and a related many-body problem
    • Airault H., McKean H.P., Moser J. Rational and elliptic solutions of the Korteweg - de Vries equation and a related many-body problem. Commun. Pure Appl. Math. 30:(1):1977;95.
    • (1977) Commun. Pure Appl. Math. , vol.30 , Issue.1 , pp. 95
    • Airault, H.1    McKean, H.P.2    Moser, J.3
  • 11
    • 4243430445 scopus 로고
    • Thermodynamics of a one-dimensional ideal gas with fractionnal exclusion statistics
    • Murthy M.V.N., Shankar R. Thermodynamics of a one-dimensional ideal gas with fractionnal exclusion statistics. Phys. Rev. Lett. 73:1994;3331.
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 3331
    • Murthy, M.V.N.1    Shankar, R.2
  • 15
    • 0000057764 scopus 로고
    • Explicit relation of the quantum Hall effect and the Calogero-Sutherland model
    • Azuma H., Iso S. Explicit relation of the quantum Hall effect and the Calogero-Sutherland model. Phys. Lett. B. 331:1994;107.
    • (1994) Phys. Lett. B , vol.331 , pp. 107
    • Azuma, H.1    Iso, S.2
  • 18
    • 4344564550 scopus 로고
    • 'Fractional statistics' in arbitrary dimensions: A generalization of the Pauli principle
    • Haldane F.D. 'Fractional statistics' in arbitrary dimensions: a generalization of the Pauli principle. Phys. Rev. Lett. 67:1991;937.
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 937
    • Haldane, F.D.1
  • 20
    • 11744320978 scopus 로고
    • Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long ranged interactions
    • Sriram Shastry B. Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long ranged interactions. Phys. Rev. Lett. 60:1988;639.
    • (1988) Phys. Rev. Lett. , vol.60 , pp. 639
    • Sriram Shastry, B.1
  • 21
    • 0001492834 scopus 로고
    • Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory
    • Haldane F.D.M., Ha Z.N.C., Talstra J.C., Bernard D., Pasquier V. Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory. Phys. Rev. Lett. 69:1992;2021.
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 2021
    • Haldane, F.D.M.1    Ha, Z.N.C.2    Talstra, J.C.3    Bernard, D.4    Pasquier, V.5
  • 22
    • 11944271119 scopus 로고
    • Exchange operator formalism for integrable systems of particles
    • Polychronakos A.P. Exchange operator formalism for integrable systems of particles. Phys. Rev. Lett. 69:1992;703.
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 703
    • Polychronakos, A.P.1
  • 23
    • 0001718938 scopus 로고
    • Integrable systems for particles with internal degrees of freedom
    • Minahan J.A., Polychronakos A.P. Integrable systems for particles with internal degrees of freedom. Phys. Lett. B. 302:1993;299 hep-th/9206046.
    • (1993) Phys. Lett. B , vol.302 , pp. 299
    • Minahan, J.A.1    Polychronakos, A.P.2
  • 25
    • 36149036547 scopus 로고
    • Spectrum of a spin chain with inverse square exchange
    • Frahm H. Spectrum of a spin chain with inverse square exchange. J. Phys. A. 26:1993;L473.
    • (1993) J. Phys. a , vol.26 , pp. 473
    • Frahm, H.1
  • 26
    • 4243503956 scopus 로고
    • Exact spectrum of SU(n) spin chain with inverse square exchange
    • Polychronakos A.P. Exact spectrum of SU(n) spin chain with inverse square exchange. Nucl. Phys. B. 419:1994;553 hep-th/9310095.
    • (1994) Nucl. Phys. B , vol.419 , pp. 553
    • Polychronakos, A.P.1
  • 27
    • 21844513685 scopus 로고
    • Solving the 1D log gas using Jack polynomials and functional relations
    • Fendley P., Lesage F., Saleur H. Solving the 1D log gas using Jack polynomials and functional relations. J. Stat. Phys. 79:1995;799 hep-th/9405008.
    • (1995) J. Stat. Phys. , vol.79 , pp. 799
    • Fendley, P.1    Lesage, F.2    Saleur, H.3
  • 28
    • 0002786564 scopus 로고
    • Matrix models, one-dimensional fermions, and quantum chaos
    • Simons B.D., Lee P.A., Altshuler B.L. Matrix models, one-dimensional fermions, and quantum chaos. Phys. Rev. Lett. 72:1994;64.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 64
    • Simons, B.D.1    Lee, P.A.2    Altshuler, B.L.3
  • 29
    • 4243265086 scopus 로고
    • Distribution of transmission eigenvalues in disordered wires
    • Caselle M. Distribution of transmission eigenvalues in disordered wires. Phys. Rev. Lett. 74:1995;2776.
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 2776
    • Caselle, M.1
  • 30
  • 31
    • 0033235627 scopus 로고    scopus 로고
    • Seiberg-Witten theory and Calogero-Moser systems
    • D'Hoker E., Phong D.H. Seiberg-Witten theory and Calogero-Moser systems. Prog. Theor. Phys. Suppl. 135:1999;75 hep-th/9906027.
    • (1999) Prog. Theor. Phys. Suppl. , vol.135 , pp. 75
    • D'Hoker, E.1    Phong, D.H.2
  • 32
    • 84963950040 scopus 로고
    • Differential-difference operators associated to reflection groups
    • Dunkl C.F. Differential-difference operators associated to reflection groups. Trans. Am. Math. Soc. 311:1989;1.
    • (1989) Trans. Am. Math. Soc. , vol.311 , pp. 1
    • Dunkl, C.F.1
  • 33
    • 0001820970 scopus 로고
    • A class of symmetric polynomials with a parameter
    • Jack H. A class of symmetric polynomials with a parameter. Proc. R. Soc. Edinburgh Sect. A. 69:1970/1971;1-18.
    • (1970) Proc. R. Soc. Edinburgh Sect. a , vol.69 , pp. 1-18
    • Jack, H.1
  • 34
    • 84971960532 scopus 로고
    • A surface integral and symmetric functions
    • Jack H. A surface integral and symmetric functions. Proc. R. Soc. Edinburgh Sect. A. 69:(4):1972;347-364.
    • (1972) Proc. R. Soc. Edinburgh Sect. a , vol.69 , Issue.4 , pp. 347-364
    • Jack, H.1
  • 35
    • 0000094781 scopus 로고
    • Double affine Hecke algebras and Macdonald's conjectures
    • Cheredenik I. Double affine Hecke algebras and Macdonald's conjectures. Ann. Math. 141:1995;191.
    • (1995) Ann. Math. , vol.141 , pp. 191
    • Cheredenik, I.1
  • 36
    • 0038962852 scopus 로고    scopus 로고
    • Affine Hecke algebras and orthogonal polynomials
    • Séminaire Bourbaki, Vol. 1994/95
    • Macdonald I.G. Affine Hecke algebras and orthogonal polynomials. Séminaire Bourbaki, Vol. 1994/95 Astérisque. 247:1996;189.
    • (1996) Astérisque , vol.247 , pp. 189
    • Macdonald, I.G.1
  • 37
    • 0043146425 scopus 로고    scopus 로고
    • Quadratic algebras, Dunkl elements and Schubert calculus
    • Fomin S., Kirillov A.N. Quadratic algebras, Dunkl elements and Schubert calculus. Prog. Math. 172:1999;147.
    • (1999) Prog. Math. , vol.172 , pp. 147
    • Fomin, S.1    Kirillov, A.N.2
  • 38
    • 0000657023 scopus 로고
    • Invariants of the Haldane-Shastry SU(N) chain
    • Flower M., Minahan J.A. Invariants of the Haldane-Shastry SU(N) chain. Phys. Rev. Lett. 70:1993;2325 cond-mat/9208016.
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 2325
    • Flower, M.1    Minahan, J.A.2
  • 39
    • 21344489887 scopus 로고
    • Yang-Baxter equation in long range interacting system
    • Bernard D., Gaudin M., Haldane F.D., Pasquier V. Yang-Baxter equation in long range interacting system. J. Phys. A. 26:1993;5219 hep-th/9301084.
    • (1993) J. Phys. a , vol.26 , pp. 5219
    • Bernard, D.1    Gaudin, M.2    Haldane, F.D.3    Pasquier, V.4
  • 40
    • 45249131043 scopus 로고
    • Some combinatorial properties of Jack symmetric functionsl
    • Stanley R.P. Some combinatorial properties of Jack symmetric functionsl. Adv. Math. 77:1988;76-115.
    • (1988) Adv. Math. , vol.77 , pp. 76-115
    • Stanley, R.P.1
  • 41
    • 0042929806 scopus 로고
    • 2 quantum many-body system
    • 2 quantum many-body system. Nucl. Phys. B. 388:1992;671.
    • (1992) Nucl. Phys. B , vol.388 , pp. 671
    • Forrester, P.J.1
  • 42
    • 0000234320 scopus 로고
    • A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture
    • Lapointe L., Vinet L. A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture. Int. Math. Res. Notices. 1995:(9):1995;419-424.
    • (1995) Int. Math. Res. Notices , vol.1995 , Issue.9 , pp. 419-424
    • Lapointe, L.1    Vinet, L.2
  • 43
    • 0030533907 scopus 로고    scopus 로고
    • Exact operator solution of the Calogero-Sutherland model
    • Lapointe L., Vinet L. Exact operator solution of the Calogero-Sutherland model. Commun. Math. Phys. 178:(2):1996;425-452.
    • (1996) Commun. Math. Phys. , vol.178 , Issue.2 , pp. 425-452
    • Lapointe, L.1    Vinet, L.2
  • 45
    • 0011584632 scopus 로고
    • Excited states of Calogero-Sutherland model and singular vectors of the W(N) algebra
    • Awata H., Matsuo Y., Odake S., Shiraishi J. Excited states of Calogero-Sutherland model and singular vectors of the W(N) algebra. Nucl. Phys. B. 449:1995;347 hep-th/9503043.
    • (1995) Nucl. Phys. B , vol.449 , pp. 347
    • Awata, H.1    Matsuo, Y.2    Odake, S.3    Shiraishi, J.4
  • 46
    • 0043067458 scopus 로고
    • Infinite symmetry of the spin systems with inverse square interactions
    • Hikami K., Wadati M. Infinite symmetry of the spin systems with inverse square interactions. J. Phys. Soc. Japan. 62:(12):1993;4203-4217.
    • (1993) J. Phys. Soc. Japan , vol.62 , Issue.12 , pp. 4203-4217
    • Hikami, K.1    Wadati, M.2
  • 47
    • 4244151791 scopus 로고
    • Integrable systems with long range interactions, w -infinity algebra and energy spectrum
    • Hikami K., Wadati M. Integrable systems with long range interactions, w -infinity algebra and energy spectrum. Phys. Rev. Lett. 73:1994;1191.
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 1191
    • Hikami, K.1    Wadati, M.2
  • 48
    • 0031501912 scopus 로고    scopus 로고
    • A recursion and a combinatorial formula for the Jack polynomials
    • Knop F., Sahi S. A recursion and a combinatorial formula for the Jack polynomials. Invent. Math. 128:1997;9.
    • (1997) Invent. Math. , vol.128 , pp. 9
    • Knop, F.1    Sahi, S.2
  • 49
    • 0041303817 scopus 로고    scopus 로고
    • Determinantal formula and recursion for Jack polynomials
    • Lapointe L., Lascoux A., Morse J. Determinantal formula and recursion for Jack polynomials. Electron. J. Comb. 7:2000;467.
    • (2000) Electron. J. Comb. , vol.7 , pp. 467
    • Lapointe, L.1    Lascoux, A.2    Morse, J.3
  • 50
    • 0030505268 scopus 로고    scopus 로고
    • Rodrigues formula of the hi-Jack symmetric polynomials associated with the quantum Calogero model
    • Ujino H., Wadati M. Rodrigues formula of the hi-Jack symmetric polynomials associated with the quantum Calogero model. J. Phys. Soc. Japan. 65:1996;2423.
    • (1996) J. Phys. Soc. Japan , vol.65 , pp. 2423
    • Ujino, H.1    Wadati, M.2
  • 52
    • 0003711757 scopus 로고    scopus 로고
    • Dean Jacqueline B. Lewis Memorial Lectures presented at Rutgers University, American Mathematical Society
    • Symmetric Functions and Orthogonal Polynomials, Dean Jacqueline B. Lewis Memorial Lectures presented at Rutgers University, American Mathematical Society, 1998.
    • (1998) Symmetric Functions and Orthogonal Polynomials
  • 53
    • 0031586414 scopus 로고    scopus 로고
    • Rodrigues formula for the Macdonald polynomials
    • Lapointe L., Vinet L. Rodrigues formula for the Macdonald polynomials. Adv. Math. 130:1997;261.
    • (1997) Adv. Math. , vol.130 , pp. 261
    • Lapointe, L.1    Vinet, L.2
  • 54
    • 14944363471 scopus 로고
    • A new class of integrable systems and its relation to solitons
    • Ruijsenaars S.N., Schneider H. A new class of integrable systems and its relation to solitons. Ann. Phys. 170:1986;370.
    • (1986) Ann. Phys. , vol.170 , pp. 370
    • Ruijsenaars, S.N.1    Schneider, H.2
  • 55
    • 3543099119 scopus 로고
    • Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
    • Ruijsenaars S.N. Complete integrability of relativistic Calogero-Moser systems and elliptic function identities. Commun. Math. Phys. 110:1987;191.
    • (1987) Commun. Math. Phys. , vol.110 , pp. 191
    • Ruijsenaars, S.N.1
  • 56
    • 0041643629 scopus 로고    scopus 로고
    • Hidden algebraic structure of the Calogero-Sutherland model, integral formula for Jack polynomial and their relativistic analog
    • J.F. van Diejen, & L. Vinet. Springer
    • Awata H. Hidden algebraic structure of the Calogero-Sutherland model, integral formula for Jack polynomial and their relativistic analog. van Diejen J.F., Vinet L. Calogero-Moser-Sutherland Models. 2000;23 Springer.
    • (2000) Calogero-Moser-Sutherland Models , pp. 23
    • Awata, H.1
  • 57
    • 0000336545 scopus 로고
    • An exactly solvable N particle system in supersymmetric quantum mechanics
    • Freedman D.Z., Mende P.F. An exactly solvable N particle system in supersymmetric quantum mechanics. Nucl. Phys. B. 344:1990;317.
    • (1990) Nucl. Phys. B , vol.344 , pp. 317
    • Freedman, D.Z.1    Mende, P.F.2
  • 58
    • 2742571438 scopus 로고
    • Dynamical breaking of supersymmetry
    • Witten E. Dynamical breaking of supersymmetry. Nucl. Phys. B. 188:1981;513.
    • (1981) Nucl. Phys. B , vol.188 , pp. 513
    • Witten, E.1
  • 59
    • 0009322069 scopus 로고
    • Constraints on supersymmetry breaking
    • Witten E. Constraints on supersymmetry breaking. Nucl. Phys. B. 202:1982;253.
    • (1982) Nucl. Phys. B , vol.202 , pp. 253
    • Witten, E.1
  • 61
    • 0001725512 scopus 로고
    • The Calogero model: Anyonic representation, fermionic extension and supersymmetry
    • Brink L., Hansson T.H., Konstein S., Vasiliev M.A. The Calogero model: anyonic representation, fermionic extension and supersymmetry. Nucl. Phys. B. 401:1993;591 hep-th/9302023.
    • (1993) Nucl. Phys. B , vol.401 , pp. 591
    • Brink, L.1    Hansson, T.H.2    Konstein, S.3    Vasiliev, M.A.4
  • 62
    • 0032351485 scopus 로고    scopus 로고
    • Hidden algebras of the (super) Calogero and Sutherland models
    • Brink L., Turbiner A., Wyllard N. Hidden algebras of the (super) Calogero and Sutherland models. J. Math. Phys. 39:1998;1285 hep-th/9705219.
    • (1998) J. Math. Phys. , vol.39 , pp. 1285
    • Brink, L.1    Turbiner, A.2    Wyllard, N.3
  • 63
    • 0034347356 scopus 로고    scopus 로고
    • (Super)conformal many-body quantum mechanics with extended supersymmetry
    • Wyllard N. (Super)conformal many-body quantum mechanics with extended supersymmetry. J. Math. Phys. 41:2000;2826 hep-th/9910160.
    • (2000) J. Math. Phys. , vol.41 , pp. 2826
    • Wyllard, N.1
  • 64
    • 0034146062 scopus 로고    scopus 로고
    • Calogero-Moser models. V: Supersymmetry and quantum lax pair
    • Bordner A.J., Manton N.S., Sasaki R. Calogero-Moser models. V: Supersymmetry and quantum lax pair. Prog. Theor. Phys. 103:2000;463 hep-th/9910033.
    • (2000) Prog. Theor. Phys. , vol.103 , pp. 463
    • Bordner, A.J.1    Manton, N.S.2    Sasaki, R.3
  • 66
    • 0001956649 scopus 로고
    • Nonlocal conservation laws for supersymmetric KdV equation
    • Dargis P., Mathieu P. Nonlocal conservation laws for supersymmetric KdV equation. Phys. Lett. A. 176:1993;67 hep-th/9301080.
    • (1993) Phys. Lett. a , vol.176 , pp. 67
    • Dargis, P.1    Mathieu, P.2
  • 67
    • 36149042260 scopus 로고
    • Supersymmetry and spin systems
    • Nicolai H. Supersymmetry and spin systems. J. Phys. A. 9:1976;1497.
    • (1976) J. Phys. a , vol.9 , pp. 1497
    • Nicolai, H.1
  • 68
    • 0043146423 scopus 로고
    • Extensions of supersymmetric spin systems
    • Nicolai H. Extensions of supersymmetric spin systems. J. Phys. A. 10:1977;2143.
    • (1977) J. Phys. a , vol.10 , pp. 2143
    • Nicolai, H.1
  • 69
    • 0009422551 scopus 로고
    • Supersymmetry and quantum mechanics
    • Cooper F., Khare A., Sukhatme U. Supersymmetry and quantum mechanics. Phys. Rep. 251:1995;267 hep-th/9405029.
    • (1995) Phys. Rep. , vol.251 , pp. 267
    • Cooper, F.1    Khare, A.2    Sukhatme, U.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.