A generic algebra associated to certain Hecke algebras

Details A generic algebra associated to certain Hecke algebras A generic algebra associated to certain Hecke algebras

2003-05-16

arxiv.org/abs/math/0305239v1

Mathematics

Representation Theory

19 pages

Scientific paper

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.

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