Eigenvalues of Shimura Operators for Lie Superalgebras
报告人：Songhao Zhu（Rutgers University）
Abstract: A super analog of S. Sahi and G. Zhang's work is obtained partially, relating Shimura operators for Hermitian superpairs and Type BC interpolation supersymmetric polynomials. In particular, I will focus on the pair (gl(2p|2q), gl(p|q)\oplus gl(p|q)) of Type AIII|AIII and discuss how we proved the Harish-Chandra images of the Shimura operators are scalar multiples of Sergeev and Veselov interpolation polynomials. These polynomials are the super twins of Okounkov polynomials. The proof relies on the sphericity of a family of modules which is completely proved when p=q=1 but remains partially open otherwise.