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arXiv · 1410.0427

Elementary Equivariant Modules

Mikhail Gudim
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Abstract

We study equivariant modules over $GL(V)$ over the polynomial ring $R = Sym V$. We introduce for every partition $λ$ the elementary equivariant module $M_λ$. Then we prove that any finitely generated equivariant module admits a fltration with associated graded being the direct sum of modules of only two kinds: either $M_λ$ or truncations of $M_λ$. We show that each $M_λ$ has a linear resolution and describe also the resolution of its truncations.

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Mikhail Gudim. 2014-10-02. Elementary Equivariant Modules. https://arxiv.org/abs/1410.0427

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