Projective resolutions of Weyl modules for the general linear group

Ana Paula Santana

The Schur algebra for the general linear group has finite global dimension.  So one can try to construct explicit projective resolutions of the Weyl modules for the Schur algebra. Let R be a commutative ring and denote by U^+_n(R) the  Kostant form over R of the universal enveloping algebra of the Lie algebra of  n x n complex nilpotent upper triangular matrices. In this talk I will explain the construction of   functors that map (minimal) projective resolutions of the rank-one trivial U^+_n(R)-module  to (minimal) projective resolutions of  rank-one modules for the Borel-Schur algebra. Using Woodcock's Theorem, from these resolutions one can easily obtain projective resolutions of the Weyl modules for the Schur algebra. This is joint work with Ivan Yudin.

Date and Venue

Start Date
Venue
Room FC1 030, Mathematics building, FCUP

Speaker

Ana Paula Santana

Speaker's Institution

CMUC, University of Coimbra

Area

Algebra, Combinatorics and Number Theory