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THE CENTER OF QUANTUM SYMMETRIC PAIR COIDEAL SUBALGEBRAS
"... Abstract. The theory of quantum symmetric pairs as developed by the second author is based on coideal subalgebras of the quantized universal enveloping algebra for a semisimple Lie algebra. This paper investigates the center of these coideal subalgebras, proving that the center is a polynomial ring. ..."
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Abstract. The theory of quantum symmetric pairs as developed by the second author is based on coideal subalgebras of the quantized universal enveloping algebra for a semisimple Lie algebra. This paper investigates the center of these coideal subalgebras, proving that the center is a polynomial ring. A basis of the center is given in terms of a submonoid of the dominant integral weights.
QUANTUM SYMMETRIC PAIRS AND REPRESENTATIONS OF DOUBLE AFFINE HECKE ALGEBRAS OF TYPE (C ∨ n, Cn)
, 908
"... Abstract. We build representations of the affine and double affine braid groups and Hecke algebras of type (C ∨ n, Cn), based upon the theory of quantum symmetric pairs (U, B). In the case U = Uq(glN), our constructions provide a quantization of the representations constructed by Etingof, Freund and ..."
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Abstract. We build representations of the affine and double affine braid groups and Hecke algebras of type (C ∨ n, Cn), based upon the theory of quantum symmetric pairs (U, B). In the case U = Uq(glN), our constructions provide a quantization of the representations constructed by Etingof, Freund and Ma in arXiv:0801.1530, and also a type BC generalization of the results in arXiv:0805.2766. 1.
JACK POLYNOMIALS FOR THE BCn ROOT SYSTEM AND GENERALIZED SPHERICAL FUNCTIONS
, 2002
"... Functions on a homogeneous space G/K invariant with respect to the left action of K are called spherical functions (or sometimes Kspherical). One can also study functions on G/K with values in a representation V of G which are equivariant with respect to the left action of K. This more ..."
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Functions on a homogeneous space G/K invariant with respect to the left action of K are called spherical functions (or sometimes Kspherical). One can also study functions on G/K with values in a representation V of G which are equivariant with respect to the left action of K. This more
PoissonLie interpretation of trigonometric Ruijsenaars duality
, 906
"... A geometric interpretation of the duality between two real forms of the complex trigonometric RuijsenaarsSchneider model is presented. The phase spaces of the models in duality are realized as two different gauge slices in the same inverse image of the moment map defining a suitable symplectic redu ..."
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A geometric interpretation of the duality between two real forms of the complex trigonometric RuijsenaarsSchneider model is presented. The phase spaces of the models in duality are realized as two different gauge slices in the same inverse image of the moment map defining a suitable symplectic reduction of the standard Heisenberg double of U(n). The collections of commuting Hamiltonians of the models in duality are shown to descend from two families of ‘free ’ Hamiltonians on the double which are dual to each other in a PoissonLie sense. Our results give rise to a major simplification of Ruijsenaars’ proof of the crucial symplectomorphism property of the duality map. 1 1