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SUMMARY:Amit Ophir (Hebrew U.)
DTSTART:20220414T170000Z
DTEND:20220414T180000Z
DTSTAMP:20260423T024805Z
UID:UCSD_NTS/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/60/
 ">Invariant norms on the p-adic Schrödinger representation</a>\nby Amit O
 phir (Hebrew U.) as part of UCSD number theory seminar\n\nLecture held in 
 online.\n\nAbstract\nMotivated by questions about a p-adic Fourier transfo
 rm\, we study invariant norms on the p-adic Schrödinger representations o
 f Heisenberg groups. These Heisenberg groups are p-adic\, and the Schrodin
 ger representations are explicit irreducible smooth representations that p
 lay an important role in their representation theory. \nClassically\, the 
 field of coefficients is taken to be the complex numbers and\, among other
  things\, one studies the unitary completions of the representations (whic
 h are well understood). By taking the field of coefficients to be an exten
 sion of the p-adic numbers\, we can consider completions that better captu
 re the p-adic topology\, but at the cost of losing the Haar measure and th
 e $L^2$-norm. Nevertheless\, we establish a rigidity property for a family
  of norms (parametrized by a Grassmannian) that are invariant under the ac
 tion of the Heisenberg group.\nThe irreducibility of some Banach represent
 ations follows as a result. The proof uses "q-arithmetics".\n\npre-talk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/60/
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