Presenting Schur superalgebras

Houssein El Turkey and Jonathan R. Kujawa

Vol. 262 (2013), No. 2, 285–316

DOI: 10.2140/pjm.2013.262.285

Abstract

We provide a presentation of the Schur superalgebra and its quantum analogue which generalizes the work of Doty and Giaquinto for Schur algebras. Our results include a basis for these algebras and a presentation using weight idempotents in the spirit of Lusztig’s modified quantum groups.

Keywords

Schur superalgebra, Lie superalgebra, Schur–Weyl duality, quantum supergroup

Mathematical Subject Classification 2010

Primary: 16S99, 20G05

Milestones

Received: 14 March 2012

Revised: 19 September 2012

Accepted: 27 September 2012

Published: 16 April 2013