Akaki Tikaradze and Apoorva Khare
نویسنده
چکیده
In this paper, we compute the center of the infinitesimal Hecke algebras Hz associated to sl2; 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 Duflo’s theorem for Hz.
منابع مشابه
Category O over a Deformation of the Symplectic Oscillator Algebra
We discuss the representation theory of Hf , which is a deformation of the symplectic oscillator algebra sp(2n) ⋉ hn, where hn is the ((2n+1)-dimensional) Heisenberg algebra. We first look at a more general algebra with a triangular decomposition. Assuming the PBW theorem, and one other hypothesis, we show that the BGG category O is abelian, finite length, and self-dual. We decompose O as a dir...
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تاریخ انتشار 2008