Seminario di algebra e geometria
ore
11:00
presso Seminario II
The algebra of invariant differential operators on a
multiplicity-free representation of a reductive group has a concrete basis,
usually referred to as the Capelli basis. The spectrum of the Capelli basis
on spherical representations results in a family of symmetric polynomials
(after \rho-shift) which has been studied extensively by Knop and Sahi in
the early 1990's. In this talk, we generalize some of the Knop-Sahi results
to the symmetric superpair GL(m,2n)/OSp(m,2n). We prove that in the
Frobenius coordinates of Sergeev-Veselov, our polynomials turn into the
shifted super Jack polynomials. This talk is based on joint work with
Siddhartha Sahi.