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
chaoping@hnu.edu.cn
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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