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SUMMARY:David Luo
DTSTART:20250930T130000Z
DTEND:20250930T140000Z
DTSTAMP:20260421T154345Z
UID:UEAPS/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/57/">O
 n the Local Converse Theorem for Depth 1/N Supercuspidal Representations o
 f $\\mathrm{GL}(2N\, F)$</a>\nby David Luo as part of ANTLR seminar\n\n\nA
 bstract\nIn this talk\, we use type theory to construct a family of depth 
 $\\frac{1}{N}$ minimax supercuspidal representations of $p$-adic $\\GL(2N\
 , F)$ which we call \\textit{middle supercuspidal representations}. These 
 supercuspidals may be viewed as a natural generalization of simple supercu
 spidal representations\, i.e. those supercuspidals of minimal positive dep
 th. Via explicit computations of twisted gamma factors\, we show that midd
 le supercuspidal representations may be uniquely determined through twisti
 ng by quasi-characters of $F^{\\times}$ and simple supercuspidal represent
 ations of $\\GL(N\, F)$. Furthermore\, we give a conjecture which refines 
 the local converse theorem for general supercuspidal representations of $\
 \GL(n\, F)$.\n
LOCATION:https://researchseminars.org/talk/UEAPS/57/
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