The affine VW supercategory

M. Balagović, Z. Daugherty, I. Entova-Aizenbud, I. Halacheva, J. Hennig, M. S. Im, G. Letzter, E. Norton, V. Serganova, C. Stroppel

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We define the affine VW supercategory [InlineEquation not available: see fulltext.], which arises from studying the action of the periplectic Lie superalgebra p(n) on the tensor product M⊗ V a of an arbitrary representation M with several copies of the vector representation V of p(n). It plays a role analogous to that of the degenerate affine Hecke algebras in the context of representations of the general linear group; the main obstacle was the lack of a quadratic Casimir element in p(n) ⊗ p(n). When M is the trivial representation, the action factors through the Brauer supercategory sBr. Our main result is an explicit basis theorem for the morphism spaces of [InlineEquation not available: see fulltext.] and, as a consequence, of sBr. The proof utilises the close connection with the representation theory of p(n). As an application we explicitly describe the centre of all endomorphism algebras, and show that it behaves well under the passage to the associated graded and under deformation.

Original languageEnglish
Article number20
JournalSelecta Mathematica, New Series
Volume26
Issue number2
DOIs
StatePublished - 1 May 2020

Keywords

  • Brauer algebras
  • Diagram algebras
  • Graded and filtered rings
  • Lie superalgebras
  • Monoidal supercategory
  • Schur–Weyl duality

ASJC Scopus subject areas

  • Mathematics (all)
  • Physics and Astronomy (all)

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