Decomposable Specht modules indexed by bihooks

Liron Speyer and Louise Sutton

Vol. 304 (2020), No. 2, 655–711

DOI: 10.2140/pjm.2020.304.655

Abstract

We study the decomposability of Specht modules labeled by bihooks, bipartitions with a hook in each component, for the Iwahori–Hecke algebra of type $B$. In all characteristics, we determine a large family of decomposable Specht modules, and conjecture that these provide a complete list of decomposable Specht modules indexed by bihooks. We prove the conjecture for small $n$.

Keywords

decomposable Specht modules, KLR algebras, quiver Hecke algebras, Specht modules, Hecke algebras

Mathematical Subject Classification 2010

Primary: 20C30, 20C08, 05E10

Milestones

Received: 13 September 2018

Revised: 17 June 2019

Accepted: 21 June 2019

Published: 12 February 2020