| Title:
|
Berezin transform for non-scalar holomorphic discrete series (English) |
| Author:
|
Cahen, Benjamin |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
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53 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
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1-17 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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, Berezin quantization for holomorphic discrete series representations: the non-scalar case, Beiträge 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 $\pi$. (English) |
| Keyword:
|
Berezin quantization |
| Keyword:
|
Berezin symbol |
| Keyword:
|
Stratonovich-Weyl correspondence |
| Keyword:
|
discrete series representation |
| Keyword:
|
Hermitian symmetric space of the non-compact type |
| Keyword:
|
semi-simple non-compact Lie group |
| Keyword:
|
coherent states |
| Keyword:
|
reproducing kernel |
| Keyword:
|
adjoint orbit |
| MSC:
|
22E46 |
| MSC:
|
32M10 |
| MSC:
|
32M15 |
| MSC:
|
81S10 |
| idZBL:
|
Zbl 1249.22008 |
| idMR:
|
MR2880907 |
| . |
| Date available:
|
2012-02-07T10:20:19Z |
| Last updated:
|
2014-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141820 |
| . |
| Reference:
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