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.

Start Date

Venue

Room FC1 030, Mathematics building, FCUP

Ana Paula Santana

CMUC, University of Coimbra

Algebra, Combinatorics and Number Theory