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SUMMARY:Ivan Ip (Hong Kong University of Science and Technology)
DTSTART:20210316T150000Z
DTEND:20210316T160000Z
DTSTAMP:20260423T024450Z
UID:GNTRT/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GNTRT/7/">Pa
 rabolic Positive Representations of $\\mathcal{U}_q(\\mathfrak{g}_\\mathbb
 {R})$</a>\nby Ivan Ip (Hong Kong University of Science and Technology) as 
 part of Geometry\, Number Theory and Representation Theory Seminar\n\n\nAb
 stract\nWe construct a new family of irreducible representations of $\\mat
 hcal{U}_q(\\mathfrak{g}_\\mathbb{R})$ and its modular double by quantizing
  the classical parabolic induction corresponding to arbitrary parabolic su
 bgroups\, such that the generators of $\\mathcal{U}_q(\\mathfrak{g}_\\math
 bb{R})$ act by positive self-adjoint operators on a Hilbert space. This ge
 neralizes the well-established positive representations introduced by [Fre
 nkel-Ip] which correspond to induction by the minimal parabolic (i.e. Bore
 l) subgroup. We also study in detail the special case of type $A_n$ acting
  on $L^2(\\mathbb{R}^n)$ with minimal functional dimension\, and establish
  the properties of its central characters and universal $\\mathcal{R}$ ope
 rator. We construct a positive version of the evaluation module of the aff
 ine quantum group\n
LOCATION:https://researchseminars.org/talk/GNTRT/7/
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