Multiplicities of weights of some representations and convex polytope
type: Item
instance of: scholarly article
title: Multiplicities of weights of some representations and convex polytope
zbMATH Open document ID: 0866.22015
DOI: 10.1007/BF01076117
author: Dmitri I. Panyushev
publication date: 1996-02-25T00:00:00Z
review text: Let \(G\) be a complex Lie group and let \(Q\) denote the root lattice of \(G\). It is shown that the polynomial \(H_\Lambda(t)\) (\(\Lambda\in Q\) being the highest root) has the property \(\deg H_\Lambda\geq\text{rk }G\) for any simple Lie group and equality holds only for \(A_p\) and \(C_p\). This coincidence suggests the idea that \(H_\Lambda(t)\) can be interpreted in terms of the weight polytope of the adjoint representation of the groups \(A_p\) and \(C_p\). The notion of laminated sequence of polytopes is introduced and all weights for the simple Lie groups are determined.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 846557
zbMATH Keywords: complex Lie group
zbMATH Keywords: root lattice
zbMATH Keywords: simple Lie group
zbMATH Keywords: weight polytope
zbMATH Keywords: representation
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
cites work: Q4040208
full work available at URL: https://doi.org/10.1007/bf01076117
OpenAlex ID: W2021554629
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 846557