TL;DR
This paper introduces a software package that constructs minimal free resolutions of certain GL_n(Q)-equivariant modules, utilizing algorithms for polynomial representations of the general linear group.
Contribution
It presents new algorithms and a software implementation for computing minimal free resolutions of specific equivariant modules over polynomial rings.
Findings
Successfully implemented algorithms for polynomial representation manipulation.
Enabled construction of minimal free resolutions with syzygies generated in a single degree.
Provides a practical tool for algebraic computations involving GL_n(Q)-equivariant modules.
Abstract
We describe a software package for constructing minimal free resolutions of GL_n(Q)-equivariant graded modules M over Q[x_1, ..., x_n] 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 GL_n(Q) following ideas of Olver and Eisenbud-Floystad-Weyman.
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