English

Untwisted Gaiotto equivalence

Representation Theory 2024-01-19 v3 Algebraic Geometry

Abstract

This is a successive paper of arXiv:1909.11492. We prove an equivalence between the category of finite-dimensional representations of degenerate supergroup GL(MN)\underline{GL}(M|N) and the category of (GLM(O)UM,N(F),χM,N)(GL_M(O) \ltimes U_{M, N}(F), \chi_{M, N})-equivariant D-modules on GrNGr_{N}. We also prove that we can realize the category of finite-dimensional representations of degenerate supergroup GL(MN)\underline{GL}(M|N) as a category of D-modules on the mirabolic subgroup MirL(F)Mir_L(F) with certain equivariant conditions for any LL bigger than NN and MM.

Keywords

Cite

@article{arxiv.2201.10462,
  title  = {Untwisted Gaiotto equivalence},
  author = {Roman Travkin and Ruotao Yang},
  journal= {arXiv preprint arXiv:2201.10462},
  year   = {2024}
}

Comments

40 pages, published version, add acknowledgements and references

R2 v1 2026-06-24T09:02:20.042Z