Quantum group of type A and representations of queer Lie superalgebra

JOURNAL OF ALGEBRA

卷:473

Article

Chen, Chih-Whi¹  Cheng, Shun-Jen² 

[1] Natl Taiwan Univ, Dept Math, Taipei 10617, Taiwan

[2] Acad Sinica, Inst Math, Taipei 10617, Taiwan

关键词: Queer Lie superalgebra;    Irreducible character;    BGG category;    Maximal parabolic subcategory;    Quantum group;    Canonical basis;    Dual canonical basis;    Brundan-Kazhdan-Lusztig conjecture;    Kac-Wakimoto character formula;    Sergeev-Pragacz character formula;   

DOI  :  10.1016/j.jalgebra.2016.10.017

来源: Elsevier

【 摘 要 】

We establish a maximal parabolic version of the Kazhdan-Lusztig conjecture [10, Conjecture 5.10] for the BGG category O-k,zeta of q(n)-modules of+/-zeta-weights, where k <= n and zeta is an element of C \ 1/2Z. As a consequence, the irreducible characters of these 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)-modules resembling polynomial and Kostant modules of the general linear Lie superalgebras are obtained. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free