Frontiers in Mathematical Sciences
7th Conference University of Isfahan  January 13, 2020 
Title:
Spherical superharmonics, singular Capelli operators, and the DougallRamanujan identity
Speaker:
Hadi Salmasian, University of Ottawa
Date, Time, and Venue: Wednesday, January 1  09:4510:30  Hall 1
Abstract:
Abstract : Given a multiplicityfree action $V$ of a simple Lie (super)algebra $g$, one can define a distinguished "Capelli" basis for the algebra of $g$invariant differential operators on $V$. The problem of computing the eigenvalues of this basis was first proposed by Kostant and Sahi, and has led to the theory of interpolation polynomials and their generalizations. In this talk, we consider an example associated to the orthosymplectic Lie superalgebras, which leads to "singular" Capelli operators, and we obtain two formulas for their eigenvalues. Along the way, the DougallRamanujan identity appears in an unexpected fashion. If time permits, we will transcend some of our results to theorems in Deligne's category $\text{Rep}(O_t).$ This talk is based on joint work with Siddhartha Sahi and Vera Serganova.
