Tilting modules for cyclotomic Schur algebras

2002/05/14 by Andrew Mathas, Mathas, Andrew · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.CO #math.GR #math.QA #math.RT #msc:20C08 #msc:20C20 #msc:20G05

paper · pdf · doi:10.48550/arxiv.math/0205143

LaTeX2e, 27 oages

arxiv created 2002/05/14 · arxiv updated 2009/11/30

Abstract

This paper investigates the tilting modules of the cyclotomic q-Schur algebras, the Young modules of the Ariki-Koike algebras, and the interconnections between them. The main tools used to understand the tilting modules are contragredient duality, and the Specht filtrations and dual Specht filtrations of certain permutation modules. Surprisingly, Weyl filtrations -- which are in general more powerful than Specht filtrations -- play only a secondary role.

Cited by

• Empty runner removal theorem for Ariki-Koike algebras
• Virtual algebraic Lie theory: Tilting modules and Ringel duals for blob algebras

Related

• The representation theory of the Ariki-Koike and cyclotomic q-Schur algebras
• On Weyl modules of cyclotomic q-Schur algebras
• Restricting Specht modules of cyclotomic Hecke algebras
• Fayers' conjecture and the socles of cyclotomic Weyl modules
• Taking tilting modules from the poset of support tilting modules