December 6, 2025Selecta MathematicaOpen Access

Parabolic-equivariant modules over polynomial rings in infinitely many variables

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This analysis finds rationality in local cohomology of P-equivariant modules, indicating deep combinatorial structures.

Rationality of the Hilbert series is established, with implications for representation categories.
Local cohomology is shown to have finite generation, enhancing existing category theory.
The category of P-equivariant modules relates closely to combinatorial categories like FI.
General linear group structures inform the behavior of these infinitely dimensional modules.

Teresa Yu (2025) studied this question.

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