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- Gail Letzter
- 1999

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 quantum homogeneous spaces. The second half discusses various well known quantum coideal subalgebras and the implications of the abstract theory on these examples. The… (More)

- Gail Letzter
- 2002

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 is proved isomorphic to the Weyl group invariants of the character group ring associated to the restricted roots. As a consequence, there is either a unique set, or… (More)

- Gail Letzter
- 2008

It is possible to develop a unified theory of quantum symmetric pairs based on a characterization of left coideal subalgebras in the quantized enveloping algebra, which are maximal with respect to specializing (in the limit) to the classical algebra fixed under an involution. Previous work established an appropriate framework for quantum zonal spherical… (More)

- Gail Letzter
- 2000

Let U denote the quantized enveloping algebra associated to a semisimple Lie algebra. This paper studies Harish-Chandra modules for the recently constructed quantum symmetric pairs U ,B in the maximally split case. Finite-dimensional U -modules are shown to be Harish-Chandra as well as the B-unitary socle of an arbitrary module. A classification of… (More)

- Anthony Joseph, Gail Letzter, SHMUEL ZELIKSON
- 2000

The base field k is assumed to be of characteristic zero. Let g be a split semisimple k-Lie algebra. Consider a finite-dimensional simple g module V and fix a weight μ of V . This paper concerns the Brylinski-Kostant (or simply, BK) filtration defined on the μ weight space of V . In particular, the members of the n subspace in the filtration are those… (More)

We analyze the centralizer of the Macdonald difference operator in an appropriate algebra of Weyl group invariant difference operators. We show that it coincides with Cherednik’s commuting algebra of difference operators via an analog of the Harish-Chandra isomorphism. Analogs of Harish-Chandra series are defined and realized as solutions to the system of… (More)

As is well known, the Shapovalov bilinear form and its determinant is an important tool in the representation theory of semisimple Lie algebras over char. 0. To our knowledge, the corresponding study of the Shapovalov bilinear form and its determinant is not available in the literature in char. p or the quantum case at roots of unity. The aim of this paper… (More)

- Gail Letzter
- 2004

The two papers in this series analyze quantum invariant differential operators for quantum symmetric spaces in the maximally split case. In this paper, we complete the proof of a quantum version of Harish-Chandra’s theorem: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and a ring of… (More)

- Dave Witte Morris, Gail Letzter, Joseph A. Gallian
- Discrete Mathematics
- 1983

- Gail Letzter
- 2004

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 induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of… (More)