BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Monica Nevins (University of Ottawa) DTSTART:20201018T160000Z DTEND:20201018T163000Z DTSTAMP:20260418T110731Z UID:MRTC2020/13 DESCRIPTION:Title: Interpreting the Harish-Chandra—Howe local character expansion via bra nching rules\nby Monica Nevins (University of Ottawa) as part of The 2 020 Paul J. Sally\, Jr. Midwest Representation Theory Conference\n\n\nAbst ract\nThe Harish-Chandra–Howe local character expansion expresses the ch aracter of an admissible representation of a $p$-adic group $G$ as a linea r combination of Fourier transforms of nilpotent orbital integrals $\\wide hat{\\mu}_{\\mathcal{O}}$ near the identity. We show that for $G=\\mathrm {SL}(2\,k)$\, where the branching rules to maximal compact open subgroups $K$ are known\, each of these terms $\\widehat{\\mu}_{\\mathcal{O}}$ can b e interpreted as the character $\\tau_{\\mathcal{O}}$ of an infinite sum o f representations of $K$\, up to an error term arising from the zero orbit . Moreover\, the irreducible components of $\\tau_{\\mathcal{O}}$ are exp licitly constructed from the $K$ -orbits in $\\mathcal{O}$. This work in progress offers a conjectural alternative interpretation of branching rule s of admissible representations.\n LOCATION:https://researchseminars.org/talk/MRTC2020/13/ END:VEVENT END:VCALENDAR