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AUSLANDER-REITEN QUIVER OF TYPE A AND GENERALIZED QUANTUM AFFINE SCHUR-WEYL DUALITY

Title
AUSLANDER-REITEN QUIVER OF TYPE A AND GENERALIZED QUANTUM AFFINE SCHUR-WEYL DUALITY
Authors
Oh, Se-Jin
Ewha Authors
오세진
SCOPUS Author ID
오세진scopus
Issue Date
2017
Journal Title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN
0002-9947JCR Link1088-6850JCR Link
Citation
vol. 369, no. 3, pp. 1895 - 1933
Publisher
AMER MATHEMATICAL SOC
Indexed
SCI; SCIE; SCOPUS WOS scopus
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-An associated to A(n) through the generalized quantum affine Schur-Weyl duality functor.
DOI
10.1090/tran6704
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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