Journal of Lie Theory

no. 3
Spin Norm, K-Types, and Tempered Representations
Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 651-658
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.
DOI: 10.5802/jolt.903
Classification: 22E46
Keywords: Dirac cohomology, K-types, spin norm, tempered representation 
@article{JOLT_2016_26_3_a1,
     author = {J. Ding and C.-P. Dong},
     title = {Spin {Norm,} {K-Types,} and {Tempered} {Representations}},
     journal = {Journal of Lie Theory},
     pages = {651--658},
     year = {2016},
     volume = {26},
     number = {3},
     doi = {10.5802/jolt.903},
     zbl = {1350.22012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.903/}
}
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J. Ding; C.-P. Dong. Spin Norm, K-Types, and Tempered Representations. Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 651-658. doi: 10.5802/jolt.903

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