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On classifying unitary modules by their Dirac cohomology

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Abstract

Let G be a connected real reductive group with maximal compact subgroup K of the same rank as G. Dirac cohomology of an A q(λ) module can be identified with a geometric object—the t-dominant part of a face of the convex hull of the Weyl group orbit of the parameter λ + ρ. We show how Dirac cohomology can be used as a parameter to classify the A q(λ) modules.

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Acknowledgements

This work was supported by Research Grant Council of Hong Kong Special Administrative Region (Grant No. 16302114) and National Natural Science Foundation of China (Grant No. 11271228), the Croatian Science Foundation (Grant No. 4176), the Center of Excellence QuantiXLie, and National Science Foundation of USA (Grant No. DMS 0967272). Parts of this work were done during the second author's visits to the Hong Kong University of Science and Technology.

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China

    Jing-Song Huang

  2. Department of Mathematics, University of Zagreb, Zagreb, 10000, Croatia

    Pavle Pandžić

  3. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    David Vogan

Authors
  1. Jing-Song Huang
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  2. Pavle Pandžić
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  3. David Vogan
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Correspondence to Jing-Song Huang.

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Dedicated to the memory of CHENG MinDe at the centenary of his birth

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Huang, JS., Pandžić, P. & Vogan, D. On classifying unitary modules by their Dirac cohomology. Sci. China Math. 60, 1937–1962 (2017). https://doi.org/10.1007/s11425-017-9097-8

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  • DOI: https://doi.org/10.1007/s11425-017-9097-8

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