Gail Letzter

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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)
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)
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)
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)
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)
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)