Representations of Brauer category and categorification

JOURNAL OF ALGEBRA

卷:557

Article

Rui, Hebing¹  Song, Linliang¹ 

[1] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

关键词: Brauer category;    Brauer algebra;    Categorification;   

DOI  :  10.1016/j.jalgebra.2020.04.013

来源: Elsevier

【 摘 要 】

We study representations of the locally unital and locally finite dimensional algebra B associated to the Brauer category B(delta(0)) with defining parameter delta(0) over an algebraically closed field K with characteristic p not equal 2. The Grothendieck group K-0(B-mod(Delta)) will be used to categorify the integrable highest weight sl(K)-module V (pi delta(0) - 1/2) with the fundamental weight pi delta(0) - 1/2 as its highest weight, where B-mod(Delta) is a subcategory of B-lfdmod in which each object has a finite Delta-flag, and sl(K) is either sl(infinity) or sl(p) depending on whether p = 0 or 2 inverted iota p. As g-modules, C circle times(Z) K-0(B-mod(Delta)) is isomorphic to V (pi delta(0) - 1/2), where g is a Lie subalgebra of sl(K) (see Definition 4.2). When p = 0, standard B-modules and projective covers of simple B-modules correspond to monomial basis and so-called quasicanonical basis of V (pi delta(0) - 1/2), respectively. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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