Norm estimates for unitarizable highest weight modules

Bernhard Krötz

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 4, page 1241-1264
  • ISSN: 0373-0956

Abstract

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We consider families of unitarizable highest weight modules ( ℋ λ ) λ ∈ L on a halfline L . All these modules can be realized as vector valued holomorphic functions on a bounded symmetric domain 𝒟 , and the polynomial functions form a dense subset of each module ℋ λ , λ ∈ L . In this paper we compare the norm of a fixed polynomial in two Hilbert spaces corresponding to two different parameters. As an application we obtain that for all λ ∈ L the module of hyperfunction vectors ℋ λ - ∞ can be realized as the space of all holomorphic functions on 𝒟 .

How to cite

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Krötz, Bernhard. "Norm estimates for unitarizable highest weight modules." Annales de l'institut Fourier 49.4 (1999): 1241-1264. <http://eudml.org/doc/75380>.

@article{Krötz1999,
abstract = {We consider families of unitarizable highest weight modules $(\{\cal H\}_\lambda )_\{\lambda \in L\}$ on a halfline $L$. All these modules can be realized as vector valued holomorphic functions on a bounded symmetric domain $\{\cal D\}$, and the polynomial functions form a dense subset of each module $\{\cal H\}_\lambda $, $\lambda \in L$. In this paper we compare the norm of a fixed polynomial in two Hilbert spaces corresponding to two different parameters. As an application we obtain that for all $\lambda \in L$ the module of hyperfunction vectors $\{\cal H\}_\lambda ^\{-\infty \}$ can be realized as the space of all holomorphic functions on $\{\cal D\}$.},
author = {Krötz, Bernhard},
journal = {Annales de l'institut Fourier},
keywords = {highest weight module; unitary representation; semisimple Lie group; semisimple Lie algebra; hermitian Lie algebra; bounded symmetric domain},
language = {eng},
number = {4},
pages = {1241-1264},
publisher = {Association des Annales de l'Institut Fourier},
title = {Norm estimates for unitarizable highest weight modules},
url = {http://eudml.org/doc/75380},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Krötz, Bernhard
TI - Norm estimates for unitarizable highest weight modules
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 4
SP - 1241
EP - 1264
AB - We consider families of unitarizable highest weight modules $({\cal H}_\lambda )_{\lambda \in L}$ on a halfline $L$. All these modules can be realized as vector valued holomorphic functions on a bounded symmetric domain ${\cal D}$, and the polynomial functions form a dense subset of each module ${\cal H}_\lambda $, $\lambda \in L$. In this paper we compare the norm of a fixed polynomial in two Hilbert spaces corresponding to two different parameters. As an application we obtain that for all $\lambda \in L$ the module of hyperfunction vectors ${\cal H}_\lambda ^{-\infty }$ can be realized as the space of all holomorphic functions on ${\cal D}$.
LA - eng
KW - highest weight module; unitary representation; semisimple Lie group; semisimple Lie algebra; hermitian Lie algebra; bounded symmetric domain
UR - http://eudml.org/doc/75380
ER -

References

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