Discrete series characters and two-structures

Herb, Rebecca

doi:10.1090/S0002-9947-98-01958-8

Discrete series characters and two-structures

Author: Rebecca A. Herb
Journal: Trans. Amer. Math. Soc. 350 (1998), 3341-3369
MSC (1991): Primary 22E30, 22E45
DOI: https://doi.org/10.1090/S0002-9947-98-01958-8
MathSciNet review: 1422607
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Abstract: Let $G$ be a connected semisimple real Lie group with compact Cartan subgroup. Harish-Chandra gave formulas for discrete series characters which are completely explicit except for certain interger constants appearing in the numerators. The main result of this paper is a new formula for these constants using two-structures. The new formula avoids endoscopy and stable discrete series entirely, expressing (unaveraged) discrete series constants directly in terms of (unaveraged) discrete series constants corresponding to two-structures of noncompact type.

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