Modular representations and branching rules for wreath Hecke algebras

Details Modular representations and branching rules for wreath Hecke algebras Modular representations and branching rules for wreath Hecke algebras

2008-06-02

arxiv.org/abs/0806.0196v2

Int. Math. Res. Not. (2008), Article ID: rnn128-31, 31 pages.

Mathematics

Representation Theory

23 pages, v2, corrections of typos and change of notation on group action, to appear in IMRN

Scientific paper

We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are classified over an algebraically closed field of any characteristic p. The modular branching rules for these algebras are obtained, and when p does not divide the order of G, they are further identified with crystal graphs of integrable modules for quantum affine algebras. The key is to establish an equivalence between a module category of the (cyclotomic) wreath Hecke algebra and its suitable counterpart for the degenerate affine Hecke algebra.

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