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Letters in Mathematical Physics

, Volume 95, Issue 1, pp 89–107 | Cite as

Dirac Induction for Loop Groups

  • Hessel Posthuma
Open Access
Article

Abstract

Using a coset version of the cubic Dirac operators for affine Lie algebras, we give an algebraic construction of the Dirac induction homomorphism for loop group representations. With this, we prove a homogeneous generalization of the Weyl–Kac character formula and show compatibility with Dirac induction for compact Lie groups.

Mathematics Subject Classification (2000)

22E67 

Keywords

loop groups Dirac induction 

Notes

Acknowledgements

The author thanks the anonymous referee for valuable comments and pointing out references [15] and [21].

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands

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