Auslander-Reiten quiver and representation theories related to KLR-type Schur-Weyl duality
- 주제(키워드) Auslander-Reiten quiver , Positive roots , Convex orders , [Q]-distance , [Q]-socle , KLR algebra , Generalized KLR-type Schur-Weyl duality , Distance polynomial , Exceptional E-types
- 주제(기타) Mathematics
- 설명문(일반) [Oh, Se-jin] Ewha Womans Univ Seoul, Dept Math, Seoul 120750, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 SPRINGER HEIDELBERG
- 발행년도 2019
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000171986
- 본문언어 영어
- Published As https://dx.doi.org/10.1007/s00209-018-2093-2
초록/요약
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))).
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