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Journal of Lie Theory 26 (2016), No. 3, 651--658
Copyright Heldermann Verlag 2016

Spin Norm, K-Types, and Tempered Representations

Jian Ding
School of Mathematics and Econometrics, Hunan University, Changsha 410082, P. R. China

Chao-Ping Dong
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.

MSC: 22E46

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