@article{CM_1996__104_3_227_0, author = {Noumi, Masatoshi and Umeda, T\^oru and Wakayama, Masato}, title = {Dual pairs, spherical harmonics and a {Capelli} identity in quantum group theory}, journal = {Compositio Mathematica}, pages = {227--277}, publisher = {Kluwer Academic Publishers}, volume = {104}, number = {3}, year = {1996}, mrnumber = {1424556}, zbl = {0930.17012}, language = {en}, url = {http://archive.numdam.org/item/CM_1996__104_3_227_0/} }
TY - JOUR AU - Noumi, Masatoshi AU - Umeda, Tôru AU - Wakayama, Masato TI - Dual pairs, spherical harmonics and a Capelli identity in quantum group theory JO - Compositio Mathematica PY - 1996 SP - 227 EP - 277 VL - 104 IS - 3 PB - Kluwer Academic Publishers UR - http://archive.numdam.org/item/CM_1996__104_3_227_0/ LA - en ID - CM_1996__104_3_227_0 ER -
%0 Journal Article %A Noumi, Masatoshi %A Umeda, Tôru %A Wakayama, Masato %T Dual pairs, spherical harmonics and a Capelli identity in quantum group theory %J Compositio Mathematica %D 1996 %P 227-277 %V 104 %N 3 %I Kluwer Academic Publishers %U http://archive.numdam.org/item/CM_1996__104_3_227_0/ %G en %F CM_1996__104_3_227_0
Noumi, Masatoshi; Umeda, Tôru; Wakayama, Masato. Dual pairs, spherical harmonics and a Capelli identity in quantum group theory. Compositio Mathematica, Tome 104 (1996) no. 3, pp. 227-277. http://archive.numdam.org/item/CM_1996__104_3_227_0/
[Ab] HopfAlgebras, Cambridge Math. Tracts 74, Cambridge Univ. Press, 1980. | MR | Zbl
:[B] The diamond lemma for ring theory, Adv. Math. 29 (1978) 178-218. | MR | Zbl
:[D] Quantum groups, in Proc. Int. Cong. Math. Berkeley, 1986, pp. 798-820. | MR | Zbl
:[F] Über algebraische Modulsysteme und lineare homogene partielle Differentialgleichungen mit konstaten Koeffizienten, J. Reine Angew. Math. 140 (1911) 48-81. | EuDML | JFM | MR
:[GK] q-Deformed orthogonal and pseudo-orthogonal algebras and their representations, Lett. Math. Phys. 21 (1991) 215-220. | MR | Zbl
and :[Ha] Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras, Comm. Math. Phys. 127 (1990) 129-144. | MR | Zbl
:[HiW] A q-analogue of Capelli's identity for GL q (2), Adv. in Math. (to appear). | MR | Zbl
and :[H1] Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989) 539-570; Erratum, Trans. Amer. Math. Soc. 318 (1990) p. 823. | MR | Zbl
:[H2] Dual pairs in physics: Harmonic oscillators, photons, electrons, and singletons, in Lectures in Applied Math. vol. 21, 1985, pp. 179-207. | MR | Zbl
:[HU] The Capelli identity, the double commutant theorem, and multiplicity-free actions, Math. Ann. 290 (1991) 565-619. | MR | Zbl
and :[Ja] On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh 46 (1908) 253-281.
:[J1] A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985) 63-69. | MR | Zbl
:[J2] A q-analogue of U(gt(N + 1)), Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986) 247-252. | MR | Zbl
:[Na1] Quantum Berezinian and the classical Capelli identity, Lett. Math. Phys. 21 (1991) 123-131. | MR | Zbl
:[Na2] private communication.
:[N1] A remark on semisimple elements in Uq (sl(2, C)), Combinatorial Aspects in Representation Theory and Geometry, RIMS Kôkyûroku 765 (1991) 71-78.
:[N2] A realization of Macdonald's symmetric polynomials on quantum homogeneous spaces, in Proceedings of the 21st International Conference on Differential Geometric Methods in Theoretical Physics, Tianjin China, 1992.
:[N3] Quantum Grassmannians and q-hypergeometric series, CWI Quarterly 5 (1992) 293-307. | MR | Zbl
:[N4] Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces, to appear, Adv. Math.. | MR | Zbl
:[NUW1] A quantum analogue of the Capelli identity and an elementary differential calculas on GLq (n) Duke Math. J. 76 (1994) 567-594. | MR | Zbl
, and :[NUW2] A quantum dual pair (sl2, On) and the associated Capelli identity, Lett. Math. Phys. 34 (1995) 1-8. | MR | Zbl
, and :[O] Twisted Yangians and infinite-dimensional classical Lie algebras, in Quantum Groups, Lecture Notes in Math. 1510, Springer Verlag (1992), pp. 103-120. | MR | Zbl
:[RTF] Quantization of the Lie groups and Lie algebras, Leningrad Math. J. 1 (1990) 193-225. | MR | Zbl
Yu., and :[U] Notes on almost homogeneity, preprint (1993).
:[UW] Another look at the differential operators on quantum matrix spaces and its applications, in preparation. | Zbl
and :[Wy] The Classical Groups, their Invariants and Representations, Princeton Univ. Press, 1946. | MR | Zbl
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