A generic algebra associated to certain Hecke algebras

2003/05/16 by Stephen Doty, Doty, Stephen, Karin Erdmann +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0305239

19 pages

arxiv created 2003/05/16 · openalex publication_date 2003/05/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain "generic" Hecke algebra, infinite-dimensional in general, coming from the universal enveloping algebra of gl_n (or sl_n). The endomorphism algebras and the generic algebras are cellular. We give several equivalent descriptions of these algebras, find a number of explicit bases, and describe indexing sets for their irreducible representations.

Related

• Stratifying Hecke endomorphism algebras using exact categories
• Modules for Yokonuma-type Hecke algebras
• Cellularity of endomorphism algebras of Young permutation modules
• Cellularity of endomorphism algebras of tilting objects
• Extending Hecke endomorphism algebras at roots of unity