Quantum group of type A and representations of queer Lie superalgebra

Chih Whi Chen; Shun Jen Cheng

doi:10.1016/j.jalgebra.2016.10.017

Quantum group of type A and representations of queer Lie superalgebra

Chih Whi Chen, Shun Jen Cheng

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We establish a maximal parabolic version of the Kazhdan–Lusztig conjecture [10, Conjecture 5.10] for the BGG category O_k,ζ of q(n)-modules of “±ζ-weights”, where k≤n and ζ∈C∖Z. 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.

Original language	English
Pages (from-to)	1-28
Number of pages	28
Journal	Journal of Algebra
Volume	473
DOIs	https://doi.org/10.1016/j.jalgebra.2016.10.017
State	Published - 1 Mar 2017

Keywords

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

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title = "Quantum group of type A and representations of queer Lie superalgebra",

abstract = "We establish a maximal parabolic version of the Kazhdan–Lusztig conjecture [10, Conjecture 5.10] for the BGG category Ok,ζ of q(n)-modules of “±ζ-weights”, where k≤n and ζ∈C∖Z. 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.",

keywords = "BGG category, Brundan–Kazhdan–Lusztig conjecture, Canonical basis, Dual canonical basis, Irreducible character, Kac–Wakimoto character formula, Maximal parabolic subcategory, Quantum group, Queer Lie superalgebra, Sergeev–Pragacz character formula",

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doi = "10.1016/j.jalgebra.2016.10.017",

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TY - JOUR

T1 - Quantum group of type A and representations of queer Lie superalgebra

AU - Chen, Chih Whi

AU - Cheng, Shun Jen

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We establish a maximal parabolic version of the Kazhdan–Lusztig conjecture [10, Conjecture 5.10] for the BGG category Ok,ζ of q(n)-modules of “±ζ-weights”, where k≤n and ζ∈C∖Z. 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.

AB - We establish a maximal parabolic version of the Kazhdan–Lusztig conjecture [10, Conjecture 5.10] for the BGG category Ok,ζ of q(n)-modules of “±ζ-weights”, where k≤n and ζ∈C∖Z. 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.

KW - BGG category

KW - Brundan–Kazhdan–Lusztig conjecture

KW - Canonical basis

KW - Dual canonical basis

KW - Irreducible character

KW - Kac–Wakimoto character formula

KW - Maximal parabolic subcategory

KW - Quantum group

KW - Queer Lie superalgebra

KW - Sergeev–Pragacz character formula

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U2 - 10.1016/j.jalgebra.2016.10.017

DO - 10.1016/j.jalgebra.2016.10.017

M3 - 期刊論文

AN - SCOPUS:84994512335

SN - 0021-8693

VL - 473

SP - 1

EP - 28

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Quantum group of type A and representations of queer Lie superalgebra

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Keywords

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