On Arthur's Φ-Function

Details On Arthur's Φ-Function On Arthur's Φ-Function

2005-03-24

arxiv.org/abs/math/0503524v1

Mathematics

Representation Theory

11 pages

Scientific paper

Write $\Theta^E$ for the stable character associated to a finite dimensional representation $E$ of a connected real reductive group $G$. Let $M$ be the centralizer of a maximal torus $T$, and denote by $\Phi_M(\gm,\Theta^E)$ Arthur's extension of $ |D_M^G(\gm)|^{\half} \Theta^E(\gm)$ to $T(\R)$. In this paper we give a simple explicit expression for $\Phi_M(\gm,\Theta^E)$, when $\gm$ is elliptic in $G$.

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