
Journal of Lie Theory 26 (2016), No. 3, 651658 Copyright Heldermann Verlag 2016 Spin Norm, KTypes, and Tempered Representations Jian Ding School of Mathematics and Econometrics, Hunan University, Changsha 410082, P. R. China ChaoPing 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 HarishChandra class. Let K be a maximal compact subgroup of G. In this setting, the spin norm of any Ktype 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 Ktypes whose spin norm equals their lambda norm. Keywords: Dirac cohomology, Ktypes, spin norm, tempered representation. MSC: 22E46 [ Fulltextpdf (265 KB)] for subscribers only. 