2023/12/14 by Siddhartha Sahi, Sahi, Siddhartha, Songhao Zhu +1
Mathematics · Physics and Astronomy · #05E05 #05E10 #17B10 #17B60 #81Q60 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2312.08661
openalex publication_date 2023/12/14 · openalex created_date 2023/12/16 · openalex updated_date 2026/07/28
The Shimura operators are a certain distinguished basis for invariant differential operators on a Hermitian symmetric space. Answering a question of Shimura, Sahi and 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 (\mathfrakg,\mathfrakk) where \mathfrakg= \mathfrakgl(2p|2q) and \mathfrakk= \mathfrakgl(p|q)⊕ \mathfrakgl(p|q) and we prove their Harish-Chandra images are specializations of certain BC-supersymmetric interpolation polynomials introduced by Sergeev--Veselov.