Elementary divisors of Specht modules

Matthias Künzer and Andrew Mathas

Abstract

This paper studies the elementary divisors of Specht modules of the Iwahori-Hecke algebra of the symmetric group over the integral Laurent polynomial ring. We give a relationship between the Gram matrices of the a Specht module and its dual (and the elementary divisors when they exist) and compute the elementary divisors for the hook partitions.

Keywords: Hecke algebras; Symmetric groups; Specht modules; elementary divisors.

AMS Subject Classification: Primary 20C08; secondary 20G05, 33D80.