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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Harmonic spinors on homogeneous spaces
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by Gregory D. Landweber
Represent. Theory 4 (2000), 466-473
DOI: https://doi.org/10.1090/S1088-4165-00-00102-3
Published electronically: September 15, 2000
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Abstract:

Let $G$ be a compact, semi-simple Lie group and $H$ a maximal rank reductive subgroup. The irreducible representations of $G$ can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space $G/H$ twisted by bundles associated to the irreducible, possibly projective, representations of $H$. Here, we give a quick proof of this result, computing the index and kernel of this twisted Dirac operator using a homogeneous version of the Weyl character formula noted by Gross, Kostant, Ramond, and Sternberg, as well as recent work of Kostant regarding an algebraic version of this Dirac operator.
References
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  • Benedict Gross, Bertram Kostant, Pierre Ramond, and Shlomo Sternberg, The Weyl character formula, the half-spin representations, and equal rank subgroups, Proc. Natl. Acad. Sci. USA 95 (1998), no. 15, 8441–8442. MR 1639139, DOI 10.1073/pnas.95.15.8441
    • K B. Kostant, A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups, Duke Math. J., 100 (1999), 447–501.
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    • St S. Sternberg, Gainesville lectures on Kostant’s Dirac operator (1999), in preparation.
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Bibliographic Information
  • Gregory D. Landweber
  • Affiliation: Microsoft Research, One Microsoft Way, Redmond, Washington 98052
  • Address at time of publication: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720-5070
  • Email: gregl@msri.org
  • Received by editor(s): May 17, 2000
  • Received by editor(s) in revised form: June 20, 2000
  • Published electronically: September 15, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Represent. Theory 4 (2000), 466-473
  • MSC (2000): Primary 22E46; Secondary 17B20, 58J20
  • DOI: https://doi.org/10.1090/S1088-4165-00-00102-3
  • MathSciNet review: 1780719