Annihilators of permutation modules

2007/11/20 by Stephen Doty, Doty, Stephen, Kathryn Nyman +1
Mathematics · #20B30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0711.3219

openalex publication_date 2007/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Permutation modules are fundamental in the representation theory of symmetric groups \Sym_n and their corresponding Iwahori--Hecke algebras \He = \He(\Sym_n). We find an explicit combinatorial basis for the annihilator of a permutation module in the "integral" case -- showing that it is a cell ideal in G.E. Murphy's cell structure of \He. The same result holds whenever \He is semisimple, but may fail in the non-semisimple case.

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