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

  • Anton Khoroshkin
  • Ievgen Makedonskyi
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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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Cite

BibTeXRIS
BibTeX
@misc{khoroshkin2026generalized,
  title = {{Generalized parabolic Demazure modules and the N!/2-conjecture for two-row diagrams}},
  author = {Anton Khoroshkin and Ievgen Makedonskyi},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02749},
  eprint = {2611.02749},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02749},
}
RIS
TY  - UNPB
TI  - Generalized parabolic Demazure modules and the N!/2-conjecture for two-row diagrams
AU  - Anton Khoroshkin
AU  - Ievgen Makedonskyi
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02749
UR  - https://arxiv.org/abs/2611.02749
AB  - 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.
ER  -