Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type

@misc{bi2026monoidal,
  title = {{Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type}},
  author = {Yingjin Bi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.05184},
  eprint = {2606.05184},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.05184},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type
AU  - Yingjin Bi
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2606.05184
UR  - https://arxiv.org/abs/2606.05184
AB  - We study determinantial modules associated with open Richardson varieties of symmetric Kac--Moody type. For the seed obtained by the Bao--Ye--Ménard mutation procedure, we give an explicit bijection between its vertices and the positions complementary to the leftmost subexpression. Each initial variable is a multiplicity-one convolution factor of the corresponding determinantial module, and these determinantial modules are cluster monomials in that seed. We deduce that the quantum cluster algebra with non-invertible frozen variables embeds in the Grothendieck ring of 𝒞_w,v, with cluster monomials represented by real simple modules up to normalization. In finite ADE type, we identify the seed with Leclerc's seed and obtain a monoidal categorification after localization at the frozen variables.
ER  -