Center and representations of infinitesimal Hecke algebras of sl_2

Details Center and representations of infinitesimal Hecke algebras of sl_2 Center and representations of infinitesimal Hecke algebras of sl_2

2008-07-30

arxiv.org/abs/0807.4776v2

Mathematics

Quantum Algebra

Final form, to appear in "Communications in Algebra"; 35 pages, laTeX

Scientific paper

In this paper, we compute the center of the infinitesimal Hecke algebras Hz
associated to sl_2 ; then using nontriviality of the center, we study
representations of these algebras in the framework of the BGG category O. We
also discuss central elements in infinitesimal Hecke algebras over gl(n) and
sp(2n) for all n. We end by proving an analogue of the theorem of Duflo for Hz.

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