Dirac index and twisted characters

Dan Barbasch, Pavle Pandžić, Peter Trapa
2018 Transactions of the American Mathematical Society  
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.
doi:10.1090/tran/7318 fatcat:7hkcd3idsjh7fh5dktzynwo3zy