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SUMMARY:Justin Trias (University of East Anglia)
DTSTART:20251015T220000Z
DTEND:20251015T230000Z
DTSTAMP:20260423T024654Z
UID:UtahRTNT/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UtahRTNT/7/"
 >The universal Harish-Chandra j-function</a>\nby Justin Trias (University 
 of East Anglia) as part of University of Utah Representation Theory / Numb
 er Theory Seminar\n\nLecture held in LCB 222.\n\nAbstract\nThe Harish–Ch
 andra μ-function plays a central role in the explicit Plancherel formula 
 for a p-adic group G. It arises as the normalising factor for the Plancher
 el measure on the unitary dual of G\, and is defined through the theory of
  intertwining operators.\n\nIn this talk\, we show how to extend the const
 ruction of the μ-function—or more precisely its inverse\, the j-functio
 n—to all finitely generated representations\, and over general coefficie
 nt rings such as Z[1/p]. This leads to a universal j-function with values 
 in the Bernstein centre\, which specialises to the classical j-function.\n
 Beyond its role in harmonic analysis\, the universal j-function also encod
 es arithmetic information: it reflects aspects of the local Langlands corr
 espondence for classical groups\, via Mœglin’s criterion and its connec
 tion to reducibility points of parabolically induced representations. Time
  permitting\, we will illustrate how this perspective applies to the study
  of the local Langlands correspondence in families. This is joint work wit
 h Gil Moss.\n
LOCATION:https://researchseminars.org/talk/UtahRTNT/7/
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