Supersymmetric Shimura operators and interpolation polynomials
- Resource Type
- Working Paper
- Authors
- Sahi, Siddhartha; Zhu, Songhao
- Source
- Subject
- Mathematics - Representation Theory
Mathematics - Commutative Algebra
17B10, 17B60, 05E05, 05E10, 81Q60
- Language
The Shimura operators are a certain distinguished basis for invariant differential operators on a Hermitian symmetric space. Answering a question of Shimura, Sahi--Zhang showed that the Harish-Chandra images of these operators are specializations of certain $BC$-symmetric interpolation polynomials that were defined by Okounkov. We consider the analogs of Shimura operators for the Hermitian symmetric superpair $(\mathfrak{g},\mathfrak{k})$ where $\mathfrak{g}= \mathfrak{gl}(2p|2q)$ and $\mathfrak{k}= \mathfrak{gl}(p|q)\oplus \mathfrak{gl}(p|q)$ and we prove their Harish-Chandra images are specializations of certain $BC$-supersymmetric interpolation polynomials introduced by Sergeev--Veselov.
Comment: 21 pages