SCHUR RING AND QUASI-SIMPLE MODULES

Schur Modules and Segre Varieties

This paper is an elementary introduction to the methods of Landsberg and Manivel, [3] for finding the ideals of secant varieties to Segre varieties. We cover only the most basic topics from [3], but hope that since this is a topic which is rarely made explicit, these notes will be of some use. We assume the reader is familiar with the basic operations of multilinear algebra: tensor, symmetric, ...

Young Modules and Schur Subalgebras

Let K r be the group algebra of the symmetric group on r symbols over a eld K of prime characteristic p. This work is motivated by the problem of comparing modules in blocks of K r of a xed core and for varying weight w, where r 2 N is arbitrary. We approach this via polynomial representations of the general linear groups GL n (K) or equivalently via Schur algebras. The main part of the thesis ...

Quasi-Exact Sequence and Finitely Presented Modules

The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.

Extensions of Baer and quasi-Baer modules

Computing inclusions of Schur modules

We describe a software package for constructing minimal free resolutions ofGLn(Q)-equivariant graded modules M over Q[x1, . . . , xn] such that for all i, the ith syzygy module of M is generated in a single degree. We do so by describing some algorithms for manipulating polynomial representations of the general linear group GLn(Q) following ideas of Olver and Eisenbud– Fløystad–Weyman.