BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nishu Kumari (Indian Institute of Science) DTSTART:20211125T060000Z DTEND:20211125T070000Z DTSTAMP:20260423T004638Z UID:ARCSIN/8 DESCRIPTION:Title: F actorization of Classical Characters twisted by Roots of Unity\nby Nis hu Kumari (Indian Institute of Science) as part of ARCSIN - Algebra\, Repr esentations\, Combinatorics and Symmetric functions in INdia\n\n\nAbstract \nIn representation theory\, Schur polynomials are the characters of the i rreducible polynomial representations of the classical groups of type A\, namely $GL_n(\\mathbb{C})$. \nMotivated by a celebrated result of Kostant\ , D. Prasad considered factorization of Schur polynomials \nin $tn$ variab les\, for $t \\geq 2$\, a fixed positive integer\, \nspecialized to $(\\ex p(2 \\pi \\iota k/t) x_j)_{0 \\leq k \\leq t-1\, 1 \\leq j \\leq n}$ (Isra el J. Math.\, 2016). He characterized partitions for which these Schur pol ynomials are nonzero and showed that if the Schur polynomial is nonzero\, it factorizes into characters of smaller classical groups of Type A.\n\nWe generalize Prasad's result to the irreducible characters of classical gro ups \nof type B\, C and D\, namely $O_{2tn+1}(\\mathbb{C})\, \n\\Sp_{2tn}( \\mathbb{C})$ and $O_{2tn}(\\mathbb{C})$\, with the same specialization. \ nWe give a uniform approach for all cases. \nThe proof uses Cauchy-type de terminant formulas for these characters and involves a careful study of th e beta sets of partitions. This is joint work with Arvind Ayyer and is ava ilable at https://arxiv.org/abs/2109.11310.\n LOCATION:https://researchseminars.org/talk/ARCSIN/8/ END:VEVENT END:VCALENDAR