Walled Brauer algebras as idempotent truncations of level 2 cyclotomic quotients

JOURNAL OF ALGEBRA

卷:440

Article

Sartori, Antonio¹  Stroppel, Catharina² 

[1] Univ Freiburg, Math Inst, D-79104 Freiburg, Germany

[2] Univ Bonn, Math Inst, D-53115 Bonn, Germany

关键词: (Degenerate affine) Walled Brauer algebra;    Category O;   

DOI  :  10.1016/j.jalgebra.2015.06.018

来源: Elsevier

【 摘 要 】

We realize (via an explicit isomorphism) the walled Brauer algebra B-r,B-t (delta) for arbitrary integral parameter delta as an idempotent truncation of a level two cyclotomic degenerate affine walled Brauer algebra. The latter arises naturally in Lie theory as the endomorphism ring of so-called mixed tensor products, i.e. of a parabolic Verma module tensored with some copies of the natural representation and its dual. The result provides a method to construct central elements in the walled Brauer algebra, and also implies the Koszulity of the walled Brauer algebras if delta not equal 0. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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