Categorification and the quantum Grassmannian
Abstract
In JKS we gave an (additive) categorification of Grassmannian cluster algebras, using the category (A) of Cohen-Macaulay modules for a certain Gorenstein order A. In this paper, using a cluster tilting object in the same category (A), we construct a compatible pair (B, L), which is the data needed to define a quantum cluster algebra. We show that when (B, L) is defined from a cluster tilting object with rank 1 summands, this quantum cluster algebra is (generically) isomorphic to the corresponding quantum Grassmannian.
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