论文标题
Shimura的某些Hermitian对称超级植物的操作员
Shimura operators for certain Hermitian symmetric superpairs
论文作者
论文摘要
我们给出了S. Sahi和G. Zhang获得的结果的部分超级类似物，该结果与Shimura操作员和某些插值对称多项式相关。特别是，我们研究了这对$（\ Mathfrak {gl}（2p | 2q），\ Mathfrak {gl}（p | q）（p | q）\ oplus \ mathfrak \ Mathfrak {gl}（p | q））$，定义超级Shimura操作员$ \ Mathfrak {证明他们在Harish-Chandra同态下的图像与Sergeev和Veselov的$ bc $ bc $ interpolation supersymmetric多项式多项式，假设是一个不可约束的$ \ mathfrak {g} $ - 模块是球形的。当$ p = q = 1 $时，我们使用Quasi-Sphericity的概念证明了这一猜想，并给出（Quasi-）球形向量的显式坐标。
We give a partial super analog of a result obtained by S. Sahi and G. Zhang relating Shimura operators and certain interpolation symmetric polynomials. In particular, we study the pair $(\mathfrak{gl}(2p|2q), \mathfrak{gl}(p|q)\oplus\mathfrak{gl}(p|q))$, define the super Shimura operators in $\mathfrak{U}(\mathfrak{g})^\mathfrak{k}$, and using a new method, prove that their images under the Harish-Chandra homomorphism are proportional to Sergeev and Veselov's Type $BC$ interpolation supersymmetric polynomials, under the assumption that a family of irreducible $\mathfrak{g}$-modules are spherical. We prove this conjecture using the notion of quasi-sphericity for Kac modules when $p=q=1$, and give explicit coordinates of (quasi-)spherical vectors.
