A classification of commutative parabolic Hecke algebras

2011/10/27 by Peter Abramenko, Abramenko, Peter, James Parkinson +3
Mathematics · #20C08 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C08

paper · pdf · doi:10.48550/arxiv.1110.6214

arxiv created 2011/10/27 · arxiv updated 2011/10/31

Abstract

Let (W,S) be a Coxeter system with I⊆ S such that the parabolic subgroup W_I is finite. Associated to this data there is a Hecke algebra \scH and a parabolic Hecke algebra \scH^I=1_I\scH1_I (over a ring \ZZ[q_s]_{s∈ S}). We give a complete classification of the commutative parabolic Hecke algebras across all Coxeter types.

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