Article ID Journal Published Year Pages File Type
4584137 Journal of Algebra 2015 37 Pages PDF
Abstract

We realize (via an explicit isomorphism) the walled Brauer algebra Br,t(δ)Br,t(δ) for arbitrary integral parameter δ   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 δ≠0δ≠0.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
, ,