| Title:
|
Invariant symbolic calculus for semidirect products (English) |
| Author:
|
Cahen, Benjamin |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
253-269 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be the semidirect product $V\rtimes \,K$ where $K$ is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space $V$. Let $\pi$ be a unitary irreducible representation of $G$ which is associated by the Kirillov-Kostant method of orbits with a coadjoint orbit of $G$ whose little group is a maximal compact subgroup of $K$. We construct an invariant symbolic calculus for $\pi$, under some technical hypothesis. We give some examples including the Poincaré group. (English) |
| Keyword:
|
semidirect products |
| Keyword:
|
invariant symbolic calculus |
| Keyword:
|
coadjoint orbit |
| Keyword:
|
unitary representation |
| Keyword:
|
Berezin quantization |
| Keyword:
|
Weyl quantization |
| Keyword:
|
Poincaré group |
| MSC:
|
22D30 |
| MSC:
|
22E45 |
| MSC:
|
22E46 |
| MSC:
|
81R05 |
| MSC:
|
81S10 |
| idZBL:
|
Zbl 06940868 |
| idMR:
|
MR3815690 |
| DOI:
|
10.14712/1213-7243.2015.244 |
| . |
| Date available:
|
2018-06-28T08:49:52Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147252 |
| . |
| Reference:
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