English

The real affine Grassmannian and quantum SL(2)

Representation Theory 2024-08-23 v2

Abstract

We prove that the category of equivariant perverse sheaves on the affine Grassmannian of PGL(2, R) is highest weight and we construct the projective objects. Moreover we prove that the category of perverse sheaves on the odd component is equivalent to the principal block of Lusztig's quantum SL(2) at a primitive fourth root of unity.

Keywords

Cite

@article{arxiv.2408.00931,
  title  = {The real affine Grassmannian and quantum SL(2)},
  author = {Mark Macerato and Jeremy Taylor},
  journal= {arXiv preprint arXiv:2408.00931},
  year   = {2024}
}

Comments

Rewritten due to an important sign error

R2 v1 2026-06-28T18:01:37.856Z