Dan Barbasch, Pavle Pandzic, Peter Trapa
Published 2016-06-17Version 1
Let G be a real reductive Lie group with maximal compact sub- group K. We generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in case 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.
Dirac Index and associated cycles of Harish-Chandra modules
$\mathfrak{sl}_2$-Harish-Chandra modules for $\mathfrak{sl}_2 \ltimes L(4)$
Classification of Harish-Chandra modules over the $W$-algebra W(2,2)
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