$S{{L}_{n\prime }}$ Orthogonality Relations and Transfer

Badulescu, Alexandru Ioan

Canadian journal of mathematics, Tome 59 (2007) no. 3, pp. 449-464

Résumé

Let $\pi $ be a square integrable representation of ${G}'=\text{S}{{\text{L}}_{n}}(D)$ , with $D$ a central division algebra of finite dimension over a local field $F$ of non-zero characteristic. We prove that, on the elliptic set, the character of $\pi $ equals the complex conjugate of the orbital integral of one of the pseudocoefficients of $\pi $ . We prove also the orthogonality relations for characters of square integrable representations of ${G}'$ . We prove the stable transfer of orbital integrals between $\text{S}{{\text{L}}_{n}}(F)$ and its inner forms.

Détail

DOI : 10.4153/CJM-2007-019-8

Mots-clés : 20G05

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