Abstract
Let g0 be a simple Lie algebra of type ADE and let U'q(g) be the corresponding untwisted quantum affine algebra. We show that there exists an action of the braid group B(g0) on the quantum Grothendieck ring Kt(g) of Hernandez-Leclerc’s category (Formula Presented). Focused on the case of type AN-1, we construct a family of monoidal autofunctors (Formula Presented) on a localization TN of the category of finite-dimensional graded modules over the quiver Hecke algebra of type A∞. Under an isomorphism between the Grothendieck ring K(TN) of TN and the quantum Grothendieck ring (Formula Presented), the functors (Formula Presented) recover the action of the braid group B(AN-1). We investigate further properties of these functors.
Original language | English |
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Pages (from-to) | 13-18 |
Number of pages | 6 |
Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |
Volume | 97 |
Issue number | 3 |
DOIs | |
State | Published - 2021 |
Bibliographical note
Publisher Copyright:© 2021 The Japan Academy
Keywords
- Quantum affine algebra
- R-matrix.
- braid group action
- quantum Grothendieck ring
- quiver Hecke algebra