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Iwahori Gaiotto conjecture for cotangent type

  • Roman Travkin
  • Ruotao Yang
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Abstract

We study the Iwahori Gaiotto conjecture for cotangent types and its application to the representation theory of the (mixed, small, and Lusztig) quantum supergroups. Using local and global models and SW-Zastava spaces, we construct factorization functors and compare the Iwahori Gaiotto category with the category O of the mixed quantum supergroup. We then study the images of intersection cohomology sheaves and the metaplectic Hecke action. In type A, we describe the finite and affine monodromic categories, the corresponding Yokonuma--Hecke actions, and their role in the Kazhdan--Lusztig algorithm. The last section treats the pointwise purity.

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Cite

BibTeXRIS
BibTeX
@misc{travkin2026iwahori,
  title = {{Iwahori Gaiotto conjecture for cotangent type}},
  author = {Roman Travkin and Ruotao Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08243},
  eprint = {2610.08243},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08243},
}
RIS
TY  - UNPB
TI  - Iwahori Gaiotto conjecture for cotangent type
AU  - Roman Travkin
AU  - Ruotao Yang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08243
UR  - https://arxiv.org/abs/2610.08243
AB  - We study the Iwahori Gaiotto conjecture for cotangent types and its application to the representation theory of the (mixed, small, and Lusztig) quantum supergroups. Using local and global models and SW-Zastava spaces, we construct factorization functors and compare the Iwahori Gaiotto category with the category O of the mixed quantum supergroup. We then study the images of intersection cohomology sheaves and the metaplectic Hecke action. In type A, we describe the finite and affine monodromic categories, the corresponding Yokonuma--Hecke actions, and their role in the Kazhdan--Lusztig algorithm. The last section treats the pointwise purity.
ER  -