1999
DOI: 10.1006/jabr.1999.8015
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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 a quantum analog of U g θ which can be characterized as the unique subalgebra of the quantized enveloping algebra of g which is a maximal right coideal that specializes to U g θ .

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Cited by 174 publications
(191 citation statements)
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“…Thus, U tw q (sp 2n ) specializes to U(sp 2n ) as q → 1. The result also follows from [21,Section 6].…”
Section: −1mentioning
confidence: 52%
See 1 more Smart Citation
“…Thus, U tw q (sp 2n ) specializes to U(sp 2n ) as q → 1. The result also follows from [21,Section 6].…”
Section: −1mentioning
confidence: 52%
“…Thus, U tw q (o N ) specializes to U(o N ) as q → 1; see [12] and [31,Section 2.4]. This result also follows from [21,Section 6].…”
Section: Orthogonal Casementioning
confidence: 62%
“…We study the problem of describing all irreducible representations that occur in the restriction to B of finite-dimensional irreducible representations of U q (su (3)). In general, information about branching rules for quantum symmetric pairs (U q (g), B) as in Kolb [13] and Letzter [16,18] is relatively scarce in particular in case the coideal subalgebra depends on an additional parameter as in this paper. However see Oblomkov and Stokman [26] for partial information on the branching rules for the quantum analogue of (gl(2n), gl(n) ⊕ gl(n)).…”
Section: Introductionmentioning
confidence: 99%
“…by G. Letzter [16,[18][19][20][21] for all semisimple Lie algebras, see also [13]. The motivating example for the development for this theory was given by Koornwinder [15], who studied scalar-valued spherical functions on the quantum analogue of (SU (2), U(1)) considering twisted primitive elements in the quantised universal enveloping algebra of U q (sl (2)).…”
Section: Introductionmentioning
confidence: 99%
“…Twisted quantum loop algebras should fit in the more general framework of quantum symmetric pairs for KacMoody Lie algebras developed in [23]. This last paper presents a generalization of the work of G. Letzter [25], M. Noumi and T. Sugitani on quantum symmetric spaces [35].…”
Section: Introductionmentioning
confidence: 99%