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DTSTAMP:20250802T220812Z
DESCRIPTION:Québec-Vermont Number Theory Seminar\n\nTitle: Invariant norms 
 on the p-adic Schrodinger representation.\n\nAbstract: Motivated by questi
 ons about a p-adic Fourier transform\, we study invariant norms on the p-a
 dic Schrödinger representations of Heisenberg groups. These Heisenberg gro
 ups are p-adic\, and the Schrodinger representations are explicit irreduci
 ble smooth representations that play an important role in their representa
 tion theory. \n	Classically\, the field of coefficients is taken to be the 
 complex numbers and\, among other things\, one studies the unitary complet
 ions of the representations (which are well understood). By taking the fie
 ld of coefficients to be an extension of the p-adic numbers\, we can consi
 der completions that better capture the p-adic topology\, but at the cost 
 of losing the Haar measure and the $L^2$-norm. Nevertheless\, we establish
  a rigidity property for a family of norms (parametrized by a Grassmannian
 ) that are invariant under the action of the Heisenberg group.\n	The irredu
 cibility of some Banach representations follows as a result. The proof use
 s 'q-arithmetics'.\n\n \n\nFor Zoom details\, please contact: martinez [at
 ] crm.umontreal.ca\n\n \n
DTSTART:20220324T190000Z
DTEND:20220324T203000Z
SUMMARY:Amit Ophir (Jerusalem)
URL:/mathstat/channels/event/amit-ophir-jerusalem-3385
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