BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sandeep Varma (Tata Institute of Fundamental Research) DTSTART:20201217T140000Z DTEND:20201217T150000Z DTSTAMP:20260418T093745Z UID:NTRV/8 DESCRIPTION:Title: On residues of certain intertwinig operators\nby Sandeep Varma (Tata Inst itute of Fundamental Research) as part of Number Theory and Representation s in Valparaiso\n\n\nAbstract\nLet $\\rm G$ be a connected reductive group over a finite extension\n$F$ of $\\mathbb{Q}_p$. Let $\\rm P = M N$ be a Levi decomposition of\na maximal parabolic subgroup of $\\rm G$\, and $\\s igma$ an irreducible unitary supercuspidal representation of ${\\rm M}(F)$ . One can then consider the representation $\\text{Ind}_{{\\rm P}(F)}^{{\\ rm G}(F)} \\sigma$ (normalized parabolic induction). This induced represen tation is known to be either irreducible or of\nlength two. The question o f when it is irreducible turns out to be (conjecturally) related to local $L$-functions\, and also to poles of a family of so called intertwining op erators. \n\nBecause of this\, one would like to:\n\n(a) get expressions d escribing residues of certain families of intertwining operators\; and\n\n (b) interpret these residues suitably\, using the theory of\nendoscopy whe n applicable.\n\nThere is an approach pioneered by Freydoon Shahidi to imp lement such a programme\, which was developed further by him as well as by David Goldberg\, Steven Spallone\, Wen-Wei Li and Xiaoxiang Yu\, in sever al cases (i.e.\, for various choices of $\\rm G$ and $\\rm P$). We will di scuss (a) in the cases where $\\rm G$ is an almost simple group whose abso lute root system is of exceptional type or of types $B_n$ or $D_n$ with $n > 3$\, and where $\\rm P$ is a `Heisenberg parabolic subgroup'. If time p ermits\, partial results towards and speculations concerning (b) will be d iscussed.\n LOCATION:https://researchseminars.org/talk/NTRV/8/ END:VEVENT END:VCALENDAR