Dirac induction for loop groups
type: Item
instance of: scholarly article
title: Dirac induction for loop groups
zbMATH Open document ID: 1207.22014
published in: Letters in Mathematical Physics
publication date: 2011-01-28T00:00:00Z
full work available at URL: 107130 359287.pdf
review text: The author gives a simple algebraic construction of Dirac induction for loop groups. This construction induces finite dimensional representations of a compact Lie group \(H\) to positive energy representations of the loop group \(LG\), where \(H\subset G\) is an equal rank embedding. The main tool of the construction is a homogeneous generalization of the representation theoretic cubic Dirac operator. As an application, the author proves a homogeneous generalization of the Weyl-Kac character formula. The results of the paper are heavily influenced by the results of \textit{G. D. Landweber} [Duke Math. J. 110, No.~1, 121--160 (2001; Zbl 1018.17016)].
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 22E67
zbMATH DE Number: 5842787
zbMATH Keywords: loop group
zbMATH Keywords: Dirac induction
zbMATH Keywords: Lie algebra
zbMATH Keywords: character
author: Hessel Posthuma
MaRDI profile type: Publication
OpenAlex ID: W1974868067
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DOI: 10.1007/S11005-010-0453-X
description: scientific article; zbMATH DE number 5842787