Invariant symbolic calculus for semidirect products

Benjamin Cahen

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 2, page 253-269
  • ISSN: 0010-2628

Abstract

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Let G be the semidirect product V ⋊ K where K is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space V . Let π 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 π , under some technical hypothesis. We give some examples including the Poincaré group.

How to cite

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Cahen, Benjamin. "Invariant symbolic calculus for semidirect products." Commentationes Mathematicae Universitatis Carolinae 59.2 (2018): 253-269. <http://eudml.org/doc/294744>.

@article{Cahen2018,
abstract = {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.},
author = {Cahen, Benjamin},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {semidirect products; invariant symbolic calculus; coadjoint orbit; unitary representation; Berezin quantization; Weyl quantization; Poincaré group},
language = {eng},
number = {2},
pages = {253-269},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Invariant symbolic calculus for semidirect products},
url = {http://eudml.org/doc/294744},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Cahen, Benjamin
TI - Invariant symbolic calculus for semidirect products
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 2
SP - 253
EP - 269
AB - 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.
LA - eng
KW - semidirect products; invariant symbolic calculus; coadjoint orbit; unitary representation; Berezin quantization; Weyl quantization; Poincaré group
UR - http://eudml.org/doc/294744
ER -

References

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