# Generalized parabolic Demazure modules and the N!/2-conjecture for two-row diagrams

“Generalized parabolic Demazure modules and the N!/2-conjecture for two-row diagrams” (2026), by Anton Khoroshkin et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Anton Khoroshkin, Ievgen Makedonskyi
- Published: November 2, 2026
- Field: Mathematics
- DOI: https://doi.org/10.48550/arxiv.2611.02749
- Free PDF: https://arxiv.org/pdf/2611.02749

## Abstract

We study a family of generalized parabolic Demazure modules, i.e. of gl[x]-submodules of tensor products of integrable representations of the affine Lie algebra generated by tensor products of extremal vectors, and describe these modules by generators and relations. Realizing the Garsia--Haiman modules of two-row diagrams as fusion products of two local Weyl modules, we show that their y-graded components admit filtrations whose associated graded modules are isomorphic to tensor products of these generalized parabolic Demazure modules with the cohomology rings of Grassmannians. As a consequence, the Garsia-Haiman modules of two-row diagrams of a fixed size generate a distributive lattice, and the N!/2-conjecture holds for two-row diagrams.

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