Categorification and the quantum Grassmannian
Representation Theory
2022-07-14 v2 Quantum Algebra
Abstract
In \cite{JKS} we gave an (additive) categorification of Grassmannian cluster algebras, using the category of Cohen-Macaulay modules for a certain Gorenstein order . In this paper, using a cluster tilting object in the same category , we construct a compatible pair , which is the data needed to define a quantum cluster algebra. We show that when is defined from a cluster tilting object with rank 1 summands, this quantum cluster algebra is (generically) isomorphic to the corresponding quantum Grassmannian.
Cite
@article{arxiv.1904.07849,
title = {Categorification and the quantum Grassmannian},
author = {Bernt Tore Jensen and Alastair King and Xiuping Su},
journal= {arXiv preprint arXiv:1904.07849},
year = {2022}
}