Dirac index and twisted characters

Barbasch, Dan; Pandžić, Pavle; Trapa, Peter

doi:10.1090/tran/7318

Dirac index and twisted characters
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by Dan Barbasch, Pavle Pandžić and Peter Trapa PDF

Trans. Amer. Math. Soc. 371 (2019), 1701-1733 Request permission

Abstract:

Let $G$ be a real reductive Lie group with maximal compact subgroup $K$. We generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in cases when $G$ and $K$ do not have equal rank. We compute ordinary and twisted indices of standard modules. As applications, we study extensions of Harish-Chandra modules and twisted characters.

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