BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rekha Biswal (University of Edinburgh) DTSTART:20201119T195000Z DTEND:20201119T205000Z DTSTAMP:20260423T005850Z UID:GPRTatNU/12 DESCRIPTION:Title: Macdonald polynomials and level two Demazure modules for affine $\\mathf rak{sl}_{n+1}$\nby Rekha Biswal (University of Edinburgh) as part of G eometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nAn im portant result due to Sanderson and Ion says that characters of level one Demazure modules are specialized Macdonald polynomials. In this talk\, I w ill introduce a new class of symmetric polynomials indexed by a pair of do minant weights of $\\mathfrak{sl}_{n+1}$ which is expressed as linear comb ination of specialized symmetric Macdonald polynomials with coefficients d efined recursively. These polynomials arose in my own work while investiga ting the characters of higher level Demazure modules. Using representation theory\, we will see that these new family of polynomials interpolate bet ween characters of level one and level two Demazure modules for affine $\\ mathfrak{sl}_{n+1}$ and give rise to new results in the representation the ory of current algebras as a corollary. This is based on joint work with V yjayanthi Chari\, Peri Shereen and Jeffrey Wand.\n LOCATION:https://researchseminars.org/talk/GPRTatNU/12/ END:VEVENT END:VCALENDAR