BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Justin Trias-Batle (Imperial College London) DTSTART:20220525T150000Z DTEND:20220525T160000Z DTSTAMP:20260418T063945Z UID:LNTS/71 DESCRIPTION:Title: To wards a theta correspondence in families for type II dual pairs\nby Ju stin Trias-Batle (Imperial College London) as part of London number theory seminar\n\nLecture held in K0.18 King's building KCL.\n\nAbstract\nThis i s current work with Gil Moss. The classical local theta correspondence for p-adic reductive dual pairs defines a bijection between prescribed subset s of irreducible smooth complex representations coming from two groups (H\ ,H')\, forming a dual pair in a symplectic group. Alberto Mínguez extende d this result for type II dual pairs\, i.e. when (H\,H') is made of genera l linear groups\, to representations with coefficients in an algebraically closed field of characteristic l as long as the characteristic l does not divide the pro-orders of H and H'. For coefficients rings like Z[1/p]\, w e explain how to build a theory in families for type II dual pairs that is compatible with reduction to residue fields of the base coefficient ring\ , where central to this approach is the integral Bernstein centre. We tran slate some weaker properties of the classical correspondence\, such as com patibility with supercuspidal support\, as a morphism between the integral Bernstein centres of H and H' and interpret it for the Weil representatio n. In general\, we only know that this morphism is finite though we may ex pect it to be surjective. This would result in a closed immersion between the associated affine schemes as well as a correspondence between characte rs of the Bernstein centre.\n LOCATION:https://researchseminars.org/talk/LNTS/71/ END:VEVENT END:VCALENDAR