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SUMMARY:Nahid Walji (University of British Columbia)
DTSTART:20210520T210000Z
DTEND:20210520T220000Z
DTSTAMP:20260423T022807Z
UID:UCSD_NTS/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/38/
 ">On the conjectural decomposition of symmetric powers of automorphic repr
 esentations for GL(3) and GL(4)</a>\nby Nahid Walji (University of British
  Columbia) as part of UCSD number theory seminar\n\nLecture held in normal
 ly APM 7321\, currently online.\n\nAbstract\nLet $\\Pi$ be a cuspidal auto
 morphic representation for GL(3) over a number field. We fix an integer $k
  \\geq 2$ and we assume that the symmetric $m$th power lifts of $\\Pi$ are
  automorphic for $m \\leq k$\, cuspidal for $m < k$\, and that certain ass
 ociated Rankin–Selberg products are automorphic. In this setting\, we bo
 und the number of cuspidal isobaric summands in the $k$th symmetric power 
 lift. In particular\, we show it is bounded above by 3 for $k \\geq 7$\, a
 nd bounded above by 2 when $k \\geq 19$ with $k$ congruent to 1 mod 3. We 
 will also discuss the analogous problem for GL(4).\n\nThis will include a 
 pre-talk.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/38/
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