ANNIHILATORS OF PERMUTATION MODULES
Copyright policy )ANNIHILATORS OF PERMUTATION MODULES
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.
18 pages
- Willamette University United States
- Loyola University Chicago United States
permutation modules, Murphy bases, Representations of finite symmetric groups, Group Theory (math.GR), annihilators, representations of symmetric groups, Iwahori-Hecke algebras, Hecke algebras and their representations, Combinatorial aspects of representation theory, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Group Theory, 20B30, Mathematics - Representation Theory
permutation modules, Murphy bases, Representations of finite symmetric groups, Group Theory (math.GR), annihilators, representations of symmetric groups, Iwahori-Hecke algebras, Hecke algebras and their representations, Combinatorial aspects of representation theory, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Group Theory, 20B30, Mathematics - Representation Theory
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