TY - JOUR

T1 - Auslander–Reiten quiver and representation theories related to KLR-type Schur–Weyl duality

AU - Oh, Se jin

N1 - Funding Information:
This work was supported by NRF Grant #2016R1C1B2013135.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/2/11

Y1 - 2019/2/11

N2 - 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 Uq(E6,7,8(1)) and partial information of denominator formulas for Uq(E6,7,8(1)). We also suggest conjecture on complete denominator formulas for Uq(E6,7,8(1)).

AB - 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 Uq(E6,7,8(1)) and partial information of denominator formulas for Uq(E6,7,8(1)). We also suggest conjecture on complete denominator formulas for Uq(E6,7,8(1)).

KW - Auslander–Reiten quiver

KW - Convex orders

KW - Distance polynomial

KW - Exceptional E-types

KW - Generalized KLR-type Schur–Weyl duality

KW - KLR algebra

KW - Positive roots

KW - [Q]-distance

KW - [Q]-socle

UR - http://www.scopus.com/inward/record.url?scp=85047908074&partnerID=8YFLogxK

U2 - 10.1007/s00209-018-2093-2

DO - 10.1007/s00209-018-2093-2

M3 - Article

AN - SCOPUS:85047908074

SN - 0025-5874

VL - 291

SP - 499

EP - 554

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 1-2

ER -