Crystal structure of localized quantum unipotent coordinate category
Abstract
Abstract A localized quantum unipotent coordinate category associated with a Weyl group element is a rigid monoidal category that is obtained by applying the localization process to the category , a subcategory of the category of finite‐dimensional graded modules of a quiver Hecke algebra . We shall show that the family of the isomorphism classes (up to grading shifts) of simple objects in possesses a crystal structure and it is isomorphic to the cellular crystal associated with . As an application of this result, we shall show the connectedness of the crystal graph of an arbitrary cellular crystal.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Proceedings of the London Mathematical Society
- Volume
- 133
- Issue
- 3
- Publication date
- 1 September 2026
- Language
- EN