Stable Discrete Series Characters at Singular Elements
Canadian journal of mathematics, Tome 61 (2009) no. 6, pp. 1375-1382
Voir la notice de l'article provenant de la source Cambridge University Press
Write ${{\Theta }^{E}}$ for the stable discrete series character associated with an irreducible finite-dimensional representation $E$ of a connected real reductive group $G$ . Let $M$ be the centralizer of the split component of a maximal torus $T$ , and denote by ${{\Phi }_{M}}\left( \gamma ,\,{{\Theta }^{E}} \right)$ Arthur’s extension of $|D_{M}^{G}\,\left( \gamma\right)|{{\,}^{1/2}}\,{{\Theta }^{E}}\,\left( \gamma\right)$ to $T\left( \mathbb{R} \right)$ . In this paper we give a simple explicit expression for ${{\Phi }_{M}}\left( \gamma ,\,{{\Theta }^{E}} \right)$ when $\gamma $ is elliptic in $G$ . We do not assume $\gamma $ is regular.
Spallone, Steven. Stable Discrete Series Characters at Singular Elements. Canadian journal of mathematics, Tome 61 (2009) no. 6, pp. 1375-1382. doi: 10.4153/CJM-2009-065-x
@article{10_4153_CJM_2009_065_x,
author = {Spallone, Steven},
title = {Stable {Discrete} {Series} {Characters} at {Singular} {Elements}},
journal = {Canadian journal of mathematics},
pages = {1375--1382},
year = {2009},
volume = {61},
number = {6},
doi = {10.4153/CJM-2009-065-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2009-065-x/}
}
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