Computing with Quantized Enveloping Algebras: PBW-Type Bases, Highest-Weight Modules andR-Matrices
نویسندگان
چکیده
منابع مشابه
Computing with Quantized Enveloping Algebras: PBW-Type Bases, Highest-Weight Modules and R-Matrices
Quantized enveloping algebras have been widely studied, almost exclusively by theoretical means (see, for example, De Concini and Procesi, 1993; Jantzen, 1996; Lusztig, 1993). In this paper we consider the problem of computing with a quantized enveloping algebra. For this we need a basis of it, along with a method for computing the product of two basis elements. To this end we will use so-calle...
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Since the invention of canonical bases of quantized enveloping algebras, one of the main problems has been to establish what they look like. Explicit formulas are only known in a few cases corresponding to root systems of low rank, namely A1 (trivial), A2 ([Lusztig 90]), A3 ([Xi 99a]), and B2 ([Xi 99b]). Furthermore, there is evidence suggesting that for higher ranks the formulas become so comp...
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We construct a monomial basis of the positive part U of the quantized enveloping algebra associated to a finite–dimensional simple Lie algebra. As an application we give a simple proof of the existence and uniqueness of the canonical basis of U. 0. Introduction In [L1], Lusztig showed that the positive part U of the quantized enveloping algebra associated to a finite–dimensional simple Lie alge...
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Let g be a finite-dimensional simple Lie algebra over C of type An, and let U be the q-analogue of its universal enveloping algebra defined by Drinfel’d [4] and Jimbo [6]. According to [9, 3.5.6, 6.2.3 & 6.3.4], for each dominant weight λ in the weight lattice of g there is an irreducible, finite-dimensional highest weight U -module V (λ) with highest weight λ. Kashiwara [7] and Lusztig [8] hav...
متن کاملCanonical Bases for the Miniscule Modules of the Quantized Enveloping Algebras of Types B and D
Let g be a finite-dimensional semisimple Lie algebra over C, and let U be the qanalogue of its universal enveloping algebra defined by Drinfel’d [3] and Jimbo [5]. According to [7, 3.5.6, 6.2.3 & 6.3.4], for each dominant weight λ in the weight lattice of g there is an irreducible, finite-dimensional highest weight U -module V (λ) with highest weight λ. Kashiwara [6] and Lusztig [7, 14.4.12] ha...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2001
ISSN: 0747-7171
DOI: 10.1006/jsco.2001.0479