BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeanne Scott (Brandeis University) DTSTART:20230306T100000Z DTEND:20230306T110000Z DTSTAMP:20260423T024449Z UID:IPHT-PHM/24 DESCRIPTION:Title: Clone symmetric function theory\nby Jeanne Scott (Brandeis Universit y) as part of Séminaire de physique mathématique IPhT\n\nLecture held in Salle Claude Itzykson\, Bât. 774\, Orme des Merisiers.\n\nAbstract\nIn 1 994 S. Okada introduced a family of non-commutative polynomials satisfying a Pieri-type identity which recapitulates the branching rule of R. Stanle y's Young-Fibonacci lattice. More generally\, products of these so called "clone" Schur functions were shown to obey a non-commutative version of th e Littlewood-Richardson identity with structure constants determined combi natorially from the Young-Fibonacci lattice structure. \n\nIn this talk I' ll survey Okada's clone theory with the aim of drawing parallels with the (classical) theory of symmetric functions\, the representation theory of t he symmetric group\, and the combinatorics of the Young lattice. I'd also like to use the opportunity to report on some speculative work based on di scussions with Leonid Petrov: Specifically a new concept of total positivi ty related to clone Schur functions together with a corresponding "Stieltj es" moment problem. If there's time\, I'll pose an open problem to the aud ience of whether a matrix model can be meaningfully associated to certain clone "tau" functions.\n LOCATION:https://researchseminars.org/talk/IPHT-PHM/24/ END:VEVENT END:VCALENDAR