Parabolic-equivariant modules over polynomial rings in infinitely many variables

• Teresa Yu ^[1]
  1. [1] Department of Mathematics, Max Planck Institute for Mathematics in the Sciences, Leipzig, GermanyDepartment of Mathematics, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 1, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-025-01107-9
• Enlaces
  • Texto completo
• Resumen

  • We study the category of P-equivariant modules over the infinite variable polynomial ring, where P denotes the subgroup of the infinite general linear group GL(C∞) consisting of elements fixing a flag in C∞ with each graded piece infinite-dimensional.

    We decompose the category into simpler pieces that can be described combinatorially, and prove a number of finiteness results, such as finite generation of local cohomology and rationality of Hilbert series. Furthermore, we show that this category is equivalent to the category of representations of a particular combinatorial category generalizing FI.

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