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$\SL_n$, Orthogonality Relations and Transfer

  Published:2007-06-01
 Printed: Jun 2007
  • Alexandru Ioan Badulescu
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Abstract

Let $\pi$ be a square integrable representation of $G'=\SL_n(D)$, with $D$ a central division algebra of finite dimension over a local field $F$ \emph{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 $\SL_n(F)$ and its inner forms.
MSC Classifications: 20G05 show english descriptions Representation theory 20G05 - Representation theory
 

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