@article{CM_1995__99_3_249_0, author = {Sugitani, Tetsuya}, title = {Harmonic analysis on quantum spheres associated with representations of $U_q (\mathfrak {so}_N)$ and $q${-Jacobi} polynomials}, journal = {Compositio Mathematica}, pages = {249--281}, publisher = {Kluwer Academic Publishers}, volume = {99}, number = {3}, year = {1995}, mrnumber = {1361741}, zbl = {0872.17013}, language = {en}, url = {http://archive.numdam.org/item/CM_1995__99_3_249_0/} }
TY - JOUR AU - Sugitani, Tetsuya TI - Harmonic analysis on quantum spheres associated with representations of $U_q (\mathfrak {so}_N)$ and $q$-Jacobi polynomials JO - Compositio Mathematica PY - 1995 SP - 249 EP - 281 VL - 99 IS - 3 PB - Kluwer Academic Publishers UR - http://archive.numdam.org/item/CM_1995__99_3_249_0/ LA - en ID - CM_1995__99_3_249_0 ER -
%0 Journal Article %A Sugitani, Tetsuya %T Harmonic analysis on quantum spheres associated with representations of $U_q (\mathfrak {so}_N)$ and $q$-Jacobi polynomials %J Compositio Mathematica %D 1995 %P 249-281 %V 99 %N 3 %I Kluwer Academic Publishers %U http://archive.numdam.org/item/CM_1995__99_3_249_0/ %G en %F CM_1995__99_3_249_0
Sugitani, Tetsuya. Harmonic analysis on quantum spheres associated with representations of $U_q (\mathfrak {so}_N)$ and $q$-Jacobi polynomials. Compositio Mathematica, Tome 99 (1995) no. 3, pp. 249-281. http://archive.numdam.org/item/CM_1995__99_3_249_0/
[A] Hopf algebras, Cambridge University Press, 1980. | MR | Zbl
:[AW] Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials 54 (1985), Memoirs Amer. Math. Soc., No. 319. | MR | Zbl
and :[B] The Diamond lemma for ring theory, Adv. in Math. 29 (1978), 178-218. | MR | Zbl
:[D1] Hopf algebras and the quantum Yang-Baxter equation, Dokl. Akad. Nauk. SSSR 283 (1985), 1060-1064. | MR | Zbl
:[D2] Quantum groups, Proceedings of the International Congress of Mathematicians, Berkeley, California, USA, 1986, pp. 798-820 | MR | Zbl
:[GR] Basic hypergeometric series, Encyclopedia of Mathematics and its applications, Cambridge University Press, 1990. | MR | Zbl
and :[H] Remarks on classical invariant theory, Trans. Amer. Math. 318 (1989), 539-570; Erratum, ibid. 318 (1990) p. 823. | MR | Zbl
:[HU] The Capelli identity, the double commutant theorem, and multiplicity-free actions, Math. Ann. 290 (1991), 565-619. | MR | Zbl
and :[J1] A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), 63-69. | MR | Zbl
:[J2] Quantum R matrix for the generalized Toda system, Comm. Math. Phys. 102 (1986), 537-548. | MR | Zbl
:[K1] Continuous q-Legendre polynomials as spherical matrix elements of irreducible representations of the quantum SU(2) group, CWI Quarterly 2 (1989), 171-173. | Zbl
:[K2] Orthogonal polynomials in connection with quantum groups, in: Orthogonal Polynomials: Theory and Practice (P. Nevai, ed.), NATO ASI Series, Kluwer Academic Publishers, 1990, pp. 257-292. | MR | Zbl
:[L] Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math. 70 (1988), 237-249. | MR | Zbl
:[Na] Crystal base and a generalization of the Littlewood-Richardson Rule for the classical Lie algebras, Comm. Math. Phys. 154 (1993), 215-243. | MR | Zbl
:[N1] Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces, Adv. in Math. (to appear). | Zbl
:[N2] A realization of Macdonald's symmetric polynomials on quantum homogeneous spaces, Int. J. Mod. Phys. A (Proc. Suppl.) 3A, World Scientific, 1993, pp. 218-223.
:[N3] Quantum groups and q-orthogonal polynomials - Towards a realization of Askey-Wilson polynomials on SUq(2), in "Special Functions" (M. Kashiwara and T. Miwa, eds.), ICM-90 Satellite Conference Proceedings, Springer-Verlag, 1991, pp. 260-288. | MR | Zbl
:[NM1] Quantum 2-spheres and big q-Jacobi polynomials, Comm. Math. Phys. 128 (1990), 521-531. | MR | Zbl
and :[NM2] Spherical functions on a family of quantum 3-spheres, Compositio Mathematica 83 (1992), 19-42. | Numdam | MR | Zbl
and :[NM3] Rogers's q-ultraspherical polynomials on a quantum 2-sphere, Duke. Math. J. 63 (1991), 65-80. | MR | Zbl
and :[NM4] Askey-Wilson polynomials and the quantum group SUq(2), Proc. Japan Acad. 66 (1990), 146-149. | MR | Zbl
and :[NUW1] A quantum analogue of the Capelli identity and an elementary differential calculus on GLq(n), preprint J-Tokyo-Math 91-16 (1991). | Zbl
, and :[NUW2] A quantum dual pair (sl2, On) and the associated Capelli identity, preprint (1993).
, and :[NUW3] Dual pairs, spherical harmonics and a Capelli identity in quantum group theory, preprint (1993). | Numdam | Zbl
, and :[NYM] Finite dimensional representations of the quantum group GLq(n;C) and the zonal spherical functions on U q(n - 1)\Uq(n), Japanese J. Math. 19 (1993), 31-80. | MR | Zbl
, and :[P1] Differential calculus on quantum spheres, Lett. Math. Phys.18 (1989), 107-119. | MR | Zbl
:[P2] Quantum spheres, Lett. Math. Phys. 14 (1987), 193-202. | MR | Zbl
:[R] Finite representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra, Comm. Math. Phys. 117 (1988), 581-593. | MR | Zbl
:[RTF] Quantization of Lie groups and Lie algebras, Algebra and Analysis 1 (1989), 178-206, English transl., in Leningrad Math. J. 1 (1990), 193-225. | MR | Zbl
, and :[T] Killing forms, Harish-Chandra isomorphisms, and universal R-matrices for quantum algebras, Int. J. Mod. Phys. A vol. 7 suppl. 1B (1992), 142-147. | MR | Zbl
:[V] Special Functions and the Theory of Group Representations, Translations of Mathematical Monographs vol. 22, 1968. | MR | Zbl
:[W1] Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), 613-665. | MR | Zbl
:[W2] Differential calculus on compact matrix pseudogroups (quantum groups), Comm. Math. Phys. 122 (1980), 125-170. | MR | Zbl
:[WSW] SOq(N) covariant differential calculus on quantum spaces and quantum deformation of Schrödinger equation, Zeitschrift für Physik C - Particles and Fields 49 (1991), 439-446. | MR
, and :