BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nicolle Gonzalez (UCLA) DTSTART:20201123T200000Z DTEND:20201123T210000Z DTSTAMP:20260423T024647Z UID:YUAAS/15 DESCRIPTION:Title: A ffine Demazure crystals for nonsymmetric Macdonald polynomials.\nby Ni colle Gonzalez (UCLA) as part of York University Applied Algebra Seminar\n \n\nAbstract\nMacdonald polynomials have long been hailed as a breakthroug h in algebraic combinatorics as they simultaneously generalize both Hall-L ittlewood and Jack symmetric polynomials. The nonsymmetric Macdonald polyn omials $E_a(X\;q\,t)$ are a further generalization which contain the symme tric versions as special cases. When specialized at $t =0$ the nonsymmetri c Macdonald polynomials were shown by Bogdon and Sanderson to arise as cha racters of affine Demazure modules\, which are certain truncations of high est weight modules. In this talk\, I will describe a type A combinatorial crystal which realizes the affine Demazure module structure and recovers t he results of Bogdon and Sanderson crystal-theoretically. The construction yields a filtration of these affine crystals by finite Demazure crystals via certain embedding operators that model those of Knop and Sahi for nons ymmetric Macdonald polynomials. Thus\, we obtain an explicit combinatorial expansion of the specialized nonsymmetric Macdonald polynomials as graded sums of key polynomials. As a consequence\, we derive a new combinatorial formula for the Kostka-Foulkes polynomials. This is joint work with Sami Assaf.\n LOCATION:https://researchseminars.org/talk/YUAAS/15/ END:VEVENT END:VCALENDAR