Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Dr. Apoorva Khare |
Affiliation | : | University of California, Riverside |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
11.00 am
|
Date |
: |
Dec 17, 2008 (Wednesday) |
Title |
: |
Infinitesimal Hecke algebras |
Abstract | : |
We study families of
infinite-dimensional algebras that are similar to semisimple Lie algebras as
well as symplectic reflection algebras. Infinitesimal Hecke algebras are
deformations of semidirect product Lie algebras, and we study two families
over $\mathfrak{sl}(2)$ and $\mathfrak{gl}(2)$. Both of them have a triangular decomposition and a
nontrivial center, which allows us to define and study the BGG Category $\mathcal{O}$
over them - including a (central character) block decomposition, and an
analog of Duflo's Theorem about primitive ideals. We then discuss certain
related setups.
|