Berezin transform for non-scalar holomorphic discrete series

Commentationes mathematicae Universitatis Carolinae

Benjamin Cahen¹ 

关键词: Berezin quantization;    Berezin symbol;    Stratonovich-Weyl correspondence;    discrete series representation;    Hermitian symmetric space of the non-compact type;    semi-simple non-compact Lie group;    coherent states;    reproducing kernel;    adjoint orbit;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

Let $M=G/K$ be a Hermitian symmetric space of the non-compact type and let $\pi$ be a discrete series representation of $G$ which is holomorphically induced from a unitary irreducible representation $\rho$ of $K$. In the paper [B. Cahen, {\it Berezin quantization for holomorphic discrete series representations the non-scalar case\/}, Beitr\"age Algebra Geom., DOI 10.1007/s13366-011-0066-2], we have introduced a notion of complex-valued Berezin symbol for an operator acting on the space of $\pi$. Here we study the corresponding Berezin transform and we show that it can be extended to a large class of symbols. As an application, we construct a Stratonovich-Weyl correspondence associated with~$\pi$.

【 授权许可】

CC BY