| Title:
|
Stratonovich-Weyl correspondence for discrete series representations (English) |
| Author:
|
Cahen, Benjamin |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
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0044-8753 (print) |
| ISSN:
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1212-5059 (online) |
| Volume:
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47 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
51-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $M=G/K$ be a Hermitian symmetric space of the noncompact type and let $\pi $ be a discrete series representation of $G$ holomorphically induced from a unitary character of $K$. Following an idea of Figueroa, Gracia-Bondìa and Vàrilly, we construct a Stratonovich-Weyl correspondence for the triple $(G, \pi , M)$ by a suitable modification of the Berezin calculus on $M$. We extend the corresponding Berezin transform to a class of functions on $M$ which contains the Berezin symbol of $d\pi (X)$ for $X$ in the Lie algebra $\mathfrak{g}$ of $G$. This allows us to define and to study the Stratonovich-Weyl symbol of $d\pi (X)$ for $X\in \mathfrak{g}$. (English) |
| Keyword:
|
Stratonovich-Weyl correspondence |
| Keyword:
|
Berezin quantization |
| Keyword:
|
Berezin transform |
| Keyword:
|
semisimple Lie group |
| Keyword:
|
coadjoint orbits |
| Keyword:
|
unitary representation |
| Keyword:
|
Hermitian symmetric space of the noncompact type |
| Keyword:
|
discrete series representation |
| Keyword:
|
reproducing kernel Hilbert space |
| Keyword:
|
coherent states |
| MSC:
|
22E46 |
| MSC:
|
32M15 |
| MSC:
|
46E22 |
| MSC:
|
81S10 |
| idZBL:
|
Zbl 1240.22011 |
| idMR:
|
MR2813546 |
| . |
| Date available:
|
2011-05-23T12:19:08Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141509 |
| . |
| Reference:
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