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SUMMARY:Vincent Sécherre (Université de Versailles)
DTSTART:20201217T170000Z
DTEND:20201217T180000Z
DTSTAMP:20260416T043644Z
UID:NTRV/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTRV/9/">Sel
 fdual cuspidal representations of ${\\rm GL}(N)$ and distinction by an inn
 er involution</a>\nby Vincent Sécherre (Université de Versailles) as par
 t of Number Theory and Representations in Valparaiso\n\n\nAbstract\nLet $n
 $ be a positive integer\, $F$ be a non-Archimedean locally compact field o
 f odd residue characteristic $p$ and $G$ be an inner form of GL$(2n\,F)$. 
 This is a group of the form GL$(r\,D)$ for a positive integer $r$ and divi
 sion $F$-algebra $D$ of reduced degree $d$ such that $rd=2n$. Let $K$ be a
  quadratic extension of $F$ in the algebra of matrices of size $r$ with co
 efficients in $D$\, and $H$ be its centralizer in $G$. We study selfdual c
 uspidal representations of $G$ and their distinction by $H$\, that is\, th
 e existence of a nonzero $H$-invariant linear form on such representations
 . When $F$ has characteristic 0\, we characterize distinction by $H$ for c
 uspidal representations of $G$ in terms of their Langlands parameter\, pro
 ving in this case a conjecture by Prasad and Takloo-Bighash.\n
LOCATION:https://researchseminars.org/talk/NTRV/9/
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