Frontiers in Mathematical Sciences 7th Conference University of Isfahan - January 1-3, 2020
 Title: Spherical superharmonics, singular Capelli operators, and the Dougall-Ramanujan identity Speaker: Hadi Salmasian, University of Ottawa Date, Time, and Venue:  Wednesday, January 1 | 09:45-10:30 | Hall 1 Abstract: Abstract : Given a multiplicity-free 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 Dougall-Ramanujan 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.