On two step tensor modules of the maximal compact subgroups of inner type noncompact real simple Lie groups
type: Item
instance of: scholarly article
title: On two step tensor modules of the maximal compact subgroups of inner type noncompact real simple Lie groups
zbMATH Open document ID: 1058.22012
author: Hisaichi Midorikawa
published in: Tokyo Journal of Mathematics
publication date: 2005-01-04T00:00:00Z
review text: Let \(\Gamma_K\) be the set of all \(P_K\)-dominant integral forms on \(b_C\). The main results of the paper are: (i) Assume that \(\mu \in \Gamma_K\) is admissible. Then the multiplicity \(M(\mu)\) of \(V_{\mu}\) in the \(K\)-module \(M(\mu)\) is given by \(M(\mu) = \#\{\omega \in \Sigma_n:\omega\) is \(P_{K(\mu)}\)-highest\(\}\). (ii) Let \(\mu \in \Gamma_K\). Then there exists a standard triple \((P_K,P(\Theta),P)\) such that \(\mu \in C(\Theta)^*\). Moreover, we have \(K(\Theta) = K(\mu)\).
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E15
zbMATH DE Number: 2124826
zbMATH Keywords: tensor module
zbMATH Keywords: Lie group
zbMATH Keywords: integral form
reviewed by: Constantin Udrişte
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1244208482
OpenAlex ID: W1997019585
Wikidata QID: Q115219849
DOI: 10.3836/TJM/1244208482
description: scientific article; zbMATH DE number 2124826