Algebra Seminar
Apoorva Khare
University of California at Riverside
Infinitesimal Hecke algebras
Abstract: We study a family of infinite-dimensional algebras that are similar to semisimple Lie algebras as well as symplectic reflection algebras.
Infinitesimal Hecke algebras over sl(2) have a triangular decomposition and a nontrivial center, which yields an analogue of Duflo's Theorem
(about primitive ideals), as well as a block decomposition of the BGG Category O.
These algebras also have a quantized version, with similar representation theory; in particular, Category O has a block decomposition, even though
the center is trivial. Finally, we discuss some questions about the higher rank cases.
(Joint with A.Tikaradze, and also with W.L.Gan.)
Monday November 24, 2008 at 4:00 PM in SEO 712