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PreprintCC BY 4.0arXiv

Lusztig Parameters and Factorizations of Determinantial Modules

  • Yingjin Bi
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Abstract

We give an explicit formula for the Lusztig parameters of determinantial modules over symmetric quiver Hecke algebras. The formula applies to every Bruhat pair and every fixed reduced expression of the upper Weyl group element. In finite types A, D, and E, we identify the parameters of the modules in Ménard's seed using Demazure weaves. We then factor prefix determinantial modules into these seed modules, with multiplicities given by Lusztig cycles. We also give a criterion for recognizing monomials in this fixed seed and an explicit formula recovering their multiplicities from Lusztig parameters.

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Cite

BibTeXRIS
BibTeX
@misc{bi2026lusztig,
  title = {{Lusztig Parameters and Factorizations of Determinantial Modules}},
  author = {Yingjin Bi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12531},
  eprint = {2610.12531},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12531},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Lusztig Parameters and Factorizations of Determinantial Modules
AU  - Yingjin Bi
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12531
UR  - https://arxiv.org/abs/2610.12531
AB  - We give an explicit formula for the Lusztig parameters of determinantial modules over symmetric quiver Hecke algebras. The formula applies to every Bruhat pair and every fixed reduced expression of the upper Weyl group element. In finite types A, D, and E, we identify the parameters of the modules in Ménard's seed using Demazure weaves. We then factor prefix determinantial modules into these seed modules, with multiplicities given by Lusztig cycles. We also give a criterion for recognizing monomials in this fixed seed and an explicit formula recovering their multiplicities from Lusztig parameters.
ER  -