U. of Haifa Algebra seminar, December 24, 2020
Speaker: Amritanshu Prasad (The Institute of Mathematical Sciences, Chennai)
Topic: Schur Algebras for the Alternating Group and Koszul Duality
Place: This is an online seminar. Please email Yuval Ginosar “ginosar at math dot haifa dot ac dot il” for the Zoom ID and password.
Date: Thursday, December 24, 2020
Abstract: The commutant of the symmetric group on $d$-fold tensor space is a Schur algebra. These actions give rise to Schur-Weyl duality, which relates representations of the symmetric group $S_d$ to some homogeneous degree $d$ polynomial representations of general linear groups. On the category of representations of $S_d$, tensoring with the sign character is a very natural endofunctor. What does this correspond to for polynomial representations of $GL(n)$? The answer turns out to be related to the commutant of the alternating group in tensor space, which we call the alternating Schur algebra.