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- Title
Coherent categorification of quantum loop algebras: The SL(2) case.
- Authors
Shan, Peng; Varagnolo, Michela; Vasserot, Eric
- Abstract
We construct an equivalence of graded Abelian categories from a category of representations of the quiver-Hecke algebra of type A 1 (1) to the category of equivariant perverse coherent sheaves on the nilpotent cone of type A. We prove that this equivalence is weakly monoidal. This gives a representation-theoretic categorification of the preprojective K-theoretic Hall algebra considered by Schiffmann and Vasserot. Using this categorification, we compare the monoidal categorification of the quantum open unipotent cells of type A 1 (1) given by Kang, Kashiwara, Kim, Oh and Park in terms of quiver-Hecke algebras with the one given by Cautis and Williams in terms of equivariant perverse coherent sheaves on the affine Grassmannians.
- Subjects
ALGEBRA; REPRESENTATIONS of algebras; SHEAF theory; ABELIAN categories; CATHETER-associated urinary tract infections; GRASSMANN manifolds; HECKE algebras
- Publication
Journal für die Reine und Angewandte Mathematik, 2022, Vol 2022, Issue 792, p1
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2022-0046