Auslander-Reiten quiver of type A and generalized quantum affine Schur-Weyl duality
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Abstract:
The quiver Hecke algebra $R$ can be also understood as a generalization of the affine Hecke algebra of type $A$ in the context of the quantum affine Schur-Weyl duality by the results of Kang, Kashiwara and Kim. On the other hand, it is well known that the Auslander-Reiten (AR) quivers $\Gamma _Q$ of finite simply-laced types have a deep relation with the positive roots systems of the corresponding types. In this paper, we present explicit combinatorial descriptions for the AR-quivers $\Gamma _Q$ of finite type $A$. Using the combinatorial descriptions, we can investigate relations between finite dimensional module categories over the quantum affine algebra $U’_q(A_n^{(i)})$ $(i=1,2)$ and finite dimensional graded module categories over the quiver Hecke algebra $R_{A_n}$ associated to $A_n$ through the generalized quantum affine Schur-Weyl duality functor.References
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Additional Information
- Se-jin Oh
- Affiliation: School of Mathematics, Korea Institute for Advanced Study Seoul 130-722, Korea
- Address at time of publication: Department of Mathematics, Ewha Womans University, Seoul 120-750, Korea
- MR Author ID: 933109
- Email: sejin092@gmail.com
- Received by editor(s): May 13, 2014
- Received by editor(s) in revised form: November 14, 2014, March 10, 2015, and March 13, 2015
- Published electronically: May 3, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 1895-1933
- MSC (2010): Primary 05E10, 16T30, 17B37; Secondary 81R50
- DOI: https://doi.org/10.1090/tran6704
- MathSciNet review: 3581223