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Auslander-Reiten quiver and representation theories related to KLR-type Schur-Weyl duality
- Title
- Auslander-Reiten quiver and representation theories related to KLR-type Schur-Weyl duality
- Authors
- Oh, Se-jin
- Ewha Authors
- 오세진
- SCOPUS Author ID
- 오세진
- Issue Date
- 2019
- Journal Title
- MATHEMATISCHE ZEITSCHRIFT
- ISSN
- 0025-5874
1432-1823
- Citation
- MATHEMATISCHE ZEITSCHRIFT vol. 291, no. 1-2, pp. 499 - 554
- Keywords
- Auslander-Reiten quiver; Positive roots; Convex orders; [Q]-distance; [Q]-socle; KLR algebra; Generalized KLR-type Schur-Weyl duality; Distance polynomial; Exceptional E-types
- Publisher
- SPRINGER HEIDELBERG
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- We introduce new partial orders on the sequence positive roots and study the statistics of the poset by using Auslander-Reiten quivers for finite type ADE. Then we can prove that the statistics provide interesting information on the representation theories of KLR-algebras, quantum groups and quantum affine algebras including Dorey's rule, bases theory for quantum groups, and denominator formulas between fundamental representations. As applications, we prove Dorey's rule for quantum affine algebras U-q(E-6,7,8((1))) and partial information of denominator formulas for U-q(E-6,7,8((1))). We also suggest conjecture on complete denominator formulas for U-q(E-6,7,8((1))).
- DOI
- 10.1007/s00209-018-2093-2
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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