Geodesic
Spin Norm, K-Types, and Tempered Representations
Journal of Lie theory, Tome 26 (2016) no. 3, pp. 651-658
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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.
Classification : 22E46
Mots-clés : Dirac cohomology, K-types, spin norm, tempered representation 
@article{JLT_2016_26_3_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2016_26_3_JLT_2016_26_3_a1/}
}
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J. Ding; C.-P. Dong. Spin Norm, K-Types, and Tempered Representations. Journal of Lie theory, Tome 26 (2016) no. 3, pp. 651-658. http://geodesic.mathdoc.fr/item/JLT_2016_26_3_JLT_2016_26_3_a1/