Quantum group of type A and representations of queer Lie superalgebra

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• 关键词：17B67
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：473
• 期：Complete
• 页码：1-28
• 全文大小：570 K
• 卷排序：473

文摘

We establish a maximal parabolic version of the Kazhdan–Lusztig conjecture [10, Conjecture 5.10] for the BGG category Ok,ζOk,ζ of q(n)q(n)-modules of “±ζ  -weights”, where k≤nk≤n and ζ∈C∖12Z. As a consequence, the irreducible characters of these q(n)q(n)-modules in this maximal parabolic category are given by the Kazhdan–Lusztig polynomials of type A   Lie algebras. As an application, closed character formulas for a class of q(n)q(n)-modules resembling polynomial and Kostant modules of the general linear Lie superalgebras are obtained.