메뉴 건너뛰기




Volumn 44, Issue 1-2, 1996, Pages 59-80

Some remarks on the construction of quantum symmetric spaces

Author keywords

Askey Wilson polynomials; Casimir operator; Compact quantum group; Koornwinder's BC type Askey Wilson polynomials; Macdonald's symmetric polynomials; Quantum projective space; Quantum symmetric space; Radial part; Two sided coideal; Zonal spherical function

Indexed keywords


EID: 0010568617     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00116516     Document Type: Article
Times cited : (35)

References (39)
  • 1
    • 0001683859 scopus 로고
    • Classical orthogonal polynomials
    • C. Brzezinski, A. Draux, P. Magnus, P. Maroni, and A. Ronveaux (eds), Polynômes orthogonaux et applications, Springer, New York
    • Andrews, G. E. and Askey, R.: Classical orthogonal polynomials, in C. Brzezinski, A. Draux, P. Magnus, P. Maroni, and A. Ronveaux (eds), Polynômes orthogonaux et applications, Lecture Notes in Math. 1171, Springer, New York, 1985, pp. 36-62.
    • (1985) Lecture Notes in Math. 1171 , pp. 36-62
    • Andrews, G.E.1    Askey, R.2
  • 2
    • 0001308382 scopus 로고
    • Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
    • Askey, R. and Wilson, J.: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985), No. 319.
    • (1985) Mem. Amer. Math. Soc. , vol.54 , Issue.319
    • Askey, R.1    Wilson, J.2
  • 4
    • 0002869419 scopus 로고
    • Quantum homogeneous spaces, duality and quantum 2-spheres
    • Dijkhuizen, M. S. and Koornwinder, T. H.: Quantum homogeneous spaces, duality and quantum 2-spheres, Geom. Dedicata 52 (1994), 291-315.
    • (1994) Geom. Dedicata , vol.52 , pp. 291-315
    • Dijkhuizen, M.S.1    Koornwinder, T.H.2
  • 5
    • 0001114958 scopus 로고
    • CQG algebras: A direct algebraic approach to compact quantum groups
    • Dijkhuizen, M. S. and Koornwinder, T. H.: CQG algebras: A direct algebraic approach to compact quantum groups, Lett. Math. Phys. 32 (1994), 315-330.
    • (1994) Lett. Math. Phys. , vol.32 , pp. 315-330
    • Dijkhuizen, M.S.1    Koornwinder, T.H.2
  • 7
    • 0000481618 scopus 로고
    • Quantum groups
    • A. M. Gleason (ed.), Amer. Math. Soc., Providence, RI
    • Drinfel'd, V. G.: Quantum groups, in A. M. Gleason (ed.), Proceedings ICM Berkeley (1986), Amer. Math. Soc., Providence, RI, 1986, pp. 798-820.
    • (1986) Proceedings ICM Berkeley (1986) , pp. 798-820
    • Drinfel'd, V.G.1
  • 9
    • 84972514127 scopus 로고
    • Non-existence of homomorphisms between quantum groups
    • Hayashi, T.: Non-existence of homomorphisms between quantum groups, Tokyo J. Math. 15(2) (1992), 431-435.
    • (1992) Tokyo J. Math. , vol.15 , Issue.2 , pp. 431-435
    • Hayashi, T.1
  • 10
    • 0003239017 scopus 로고
    • Harmonic Analysis and Special Functions on Symmetric Spaces
    • Academic Press, New York
    • Heckman, G. J. and Schlichtkrull, H.: Harmonic Analysis and Special Functions on Symmetric Spaces, Perspectives in Math. 16, Academic Press, New York, 1995.
    • (1995) Perspectives in Math. 16
    • Heckman, G.J.1    Schlichtkrull, H.2
  • 11
    • 0003245418 scopus 로고
    • Differential Geometry, Lie Groups, and Symmetric Spaces
    • Academic Press, New York
    • Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces, Pure Appl. Math. 80, Academic Press, New York, 1978.
    • (1978) Pure Appl. Math. 80
    • Helgason, S.1
  • 12
    • 0002894145 scopus 로고
    • Groups and Geometric Analysis
    • Academic Press, New York
    • Helgason, S.: Groups and Geometric Analysis, Pure Appl. Math. 113, Academic Press, New York, 1984.
    • (1984) Pure Appl. Math. 113
    • Helgason, S.1
  • 13
    • 0040323775 scopus 로고
    • A q-difference analogue of U(g) and the Yang-Baxter equation
    • Jimbo, M.: A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), 63-69.
    • (1985) Lett. Math. Phys. , vol.10 , pp. 63-69
    • Jimbo, M.1
  • 14
    • 0038863258 scopus 로고
    • Quantum R-matrix for the generalized Toda system
    • Jimbo, M.: Quantum R-matrix for the generalized Toda system, Comm. Math. Phys. 102 (1986), 537-547.
    • (1986) Comm. Math. Phys. , vol.102 , pp. 537-547
    • Jimbo, M.1
  • 15
    • 0345930356 scopus 로고
    • A q-analogue of U(gl(n)), Hecke algebra and the Yang-Baxter equation
    • Jimbo, M.: A q-analogue of U(gl(n)), Hecke algebra and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), 247-252.
    • (1986) Lett. Math. Phys. , vol.11 , pp. 247-252
    • Jimbo, M.1
  • 16
    • 0007159514 scopus 로고
    • Representations of the twisted SU(2) quantum group and some q-hypergeometric orthogonal polynomials
    • Koornwinder, T. H.: Representations of the twisted SU(2) quantum group and some q-hypergeometric orthogonal polynomials, Proc. Kon. Ned. Akad. Wet. Series A 92 (1989), 97-117.
    • (1989) Proc. Kon. Ned. Akad. Wet. Series A , vol.92 , pp. 97-117
    • Koornwinder, T.H.1
  • 17
    • 0001542822 scopus 로고
    • Orthogonal polynomials in connection with quantum groups
    • P. Nevai (ed.), NATO-ASI Series C 294, Kluwer, Norwell, MA
    • Koornwinder, T. H.: Orthogonal polynomials in connection with quantum groups, in P. Nevai (ed.), Orthogonal Polynomials: Theory and Practice, NATO-ASI Series C 294, Kluwer, Norwell, MA, 1990, pp. 257-292.
    • (1990) Orthogonal Polynomials: Theory and Practice , pp. 257-292
    • Koornwinder, T.H.1
  • 18
    • 0000515270 scopus 로고
    • Askey-Wilson polynomials for root systems of type BC
    • D. S. P. Richards (ed.), Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, Amer. Math. Soc., Providence, RI
    • Koornwinder, T. H.: Askey-Wilson polynomials for root systems of type BC, in D. S. P. Richards (ed.), Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, Contemp. Math. 138, Amer. Math. Soc., Providence, RI, 1992, pp. 189-204.
    • (1992) Contemp. Math. 138 , pp. 189-204
    • Koornwinder, T.H.1
  • 19
    • 0009464049 scopus 로고
    • Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group
    • Koornwinder, T. H.: Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group, SIAM J. Math. Anal. 24(3) (1993), 795-813.
    • (1993) SIAM J. Math. Anal. , vol.24 , Issue.3 , pp. 795-813
    • Koornwinder, T.H.1
  • 20
    • 0041009450 scopus 로고
    • Quantum G-spaces and Heisenberg algebra
    • P. P. Kulish (ed.), Quantum Groups, Springer
    • Korogodsky, L. I. and Vaksman, L. L.: Quantum G-spaces and Heisenberg algebra, in P. P. Kulish (ed.), Quantum Groups, Lecture Notes in Math. 1510, Springer, 1992, pp. 56-66.
    • (1992) Lecture Notes in Math. 1510 , pp. 56-66
    • Korogodsky, L.I.1    Vaksman, L.L.2
  • 22
    • 45449122603 scopus 로고
    • Quantum deformations of certain simple modules over enveloping algebras
    • Lusztig, G.: Quantum deformations of certain simple modules over enveloping algebras, Adv. Math. 70 (1988), 237-249.
    • (1988) Adv. Math. , vol.70 , pp. 237-249
    • Lusztig, G.1
  • 23
    • 0003310111 scopus 로고
    • A new class of symmetric functions
    • L. Cerlienco and D. Foata (eds), Publication I.R.M.A. 372/S-20, Strasbourg
    • Macdonald, I. G.: A new class of symmetric functions, in L. Cerlienco and D. Foata (eds), Séminaire Lotharingien de combinatoire, Publication I.R.M.A. 372/S-20, Strasbourg, 1988, pp. 131-171.
    • (1988) Séminaire Lotharingien de Combinatoire , pp. 131-171
    • Macdonald, I.G.1
  • 25
    • 0010716039 scopus 로고
    • Affine Hecke algebras and orthogonal polynomials
    • Macdonald, I. G.: Affine Hecke algebras and orthogonal polynomials, Séminaire Bourbaki, 47(797) (1994-95), 1-18.
    • (1994) Séminaire Bourbaki , vol.47 , Issue.797 , pp. 1-18
    • Macdonald, I.G.1
  • 27
    • 0030588041 scopus 로고    scopus 로고
    • Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
    • to appear
    • Noumi, M.: Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces, Adv. Math. (to appear).
    • Adv. Math.
    • Noumi, M.1
  • 29
    • 0002047632 scopus 로고
    • Quantum symmetric spaces and related q-orthogonal polynomials
    • A. Arima et al. (eds), Group Theoretical Methods in Physics, Toyonaka (Japan), 1994, World Scientific, Singapore
    • Noumi, M. and Sugitani, T.: Quantum symmetric spaces and related q-orthogonal polynomials, in A. Arima et al. (eds), Group Theoretical Methods in Physics, Proceedings XX ICGTMP, Toyonaka (Japan), 1994, World Scientific, Singapore, 1995, pp. 28-40.
    • (1995) Proceedings XX ICGTMP , pp. 28-40
    • Noumi, M.1    Sugitani, T.2
  • 32
    • 0347062767 scopus 로고
    • Quantum spheres
    • Podleś, P.: Quantum spheres, Lett. Math. Phys. 14 (1987), 193-202.
    • (1987) Lett. Math. Phys. , vol.14 , pp. 193-202
    • Podleś, P.1
  • 34
    • 34250094247 scopus 로고
    • Finite-dimensional representations of the quantum analog of a complex simple Lie algebra
    • Rosso, M.: Finite-dimensional representations of the quantum analog of a complex simple Lie algebra, Comm. Math. Phys. 117 (1988), 581-593.
    • (1988) Comm. Math. Phys. , vol.117 , pp. 581-593
    • Rosso, M.1
  • 37
    • 0011573490 scopus 로고
    • Zonal spherical functions on quantum symmetric spaces and Macdonald's symmetric polynomials
    • P. P. Kulish (ed.), Quantum Groups, Springer, New York
    • Ueno, K. and Takebayashi, T.: Zonal spherical functions on quantum symmetric spaces and Macdonald's symmetric polynomials, in P. P. Kulish (ed.), Quantum Groups, Lecture Notes in Math. 1510, Springer, New York, 1992, pp. 142-147.
    • (1992) Lecture Notes in Math. 1510 , pp. 142-147
    • Ueno, K.1    Takebayashi, T.2
  • 38
    • 1642599685 scopus 로고
    • Algebra of functions on the quantum group SU(2)
    • Vaksman, L. L. and Soǐbel'man, Y. S.: Algebra of functions on the quantum group SU(2), Funct. Anal. Appl. 22 (1988), 170-181.
    • (1988) Funct. Anal. Appl. , vol.22 , pp. 170-181
    • Vaksman, L.L.1    Soǐbel'man, Y.S.2
  • 39
    • 1542483491 scopus 로고
    • Compact matrix pseudogroups
    • Woronowicz, S. L.: Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), 613-665.
    • (1987) Comm. Math. Phys. , vol.111 , pp. 613-665
    • Woronowicz, S.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.