Journal of Lie Theory 26 (2016), No. 3, 651--658
Copyright Heldermann Verlag 2016
Spin Norm, K-Types, and Tempered Representations
School of Mathematics and Econometrics, Hunan University, Changsha 410082, P. R. China
Institute of Mathematics, Hunan University, Changsha 410082, P. R. China
We extend the notion spin norm slightly to a real reductive Lie group G in the Harish-Chandra class. Let K be a maximal compact subgroup of G. In this setting, the spin norm of any K-type π is still bounded from below by its lambda norm. We establish a bijection between irreducible tempered (g, K)-modules with nonzero Dirac cohomology and those K-types whose spin norm equals their lambda norm.
Keywords: Dirac cohomology, K-types, spin norm, tempered representation.
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