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Coideal Subalgebras and Quantum Symmetric Pairs
Coideal subalgebras of the quantized enveloping algebra are surveyed, with selected proofs included. The first half of the paper studies generators, Harish-Chandra modules, and associated quantumExpand
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Quantum Symmetric Pairs and Their Zonal Spherical Functions
We study the space of biinvariants and zonal spherical functions associated to quantum symmetric pairs in the maximally split case. Under the obvious restriction map, the space of biinvariants isExpand
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Quantum zonal spherical functions and Macdonald polynomials
Abstract A unified theory of quantum symmetric pairs is applied to q -special functions. Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra andExpand
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Symmetric Pairs for Quantized Enveloping Algebras
Abstract Let θ be an involution of a semisimple Lie algebra g , let g θ denote the fixed Lie subalgebra, and assume the Cartan subalgebra of g has been chosen in a suitable way. We construct aExpand
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Ring theory from symplectic geometry
Abstract Basic results for an algebraic treatment of commutative and noncommutative Poisson algebras are described. Symplectic algebras are examined from a ring-theoretic point of view.
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Invariant differential operators for quantum symmetric spaces, II
This is the first paper in a series of two which proves a version of a theorem of Harish-Chandra for quantum symmetric spaces in the maximally split case: There is a Harish-Chandra map which inducesExpand
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TRANSLATION FUNCTORS AND DECOMPOSITION NUMBERS FOR THE PERIPLECTIC LIE SUPERALGEBRA p(n)
We study the category Fn of finite-dimensional integrable representations of the periplectic Lie superalgebra p(n). We define an action of the Temperley–Lieb algebra with infinitely many generatorsExpand
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