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

2015/09/16 by Oh, Se-jin
#05E10 #16T30 #17B37 #81R50 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1509.04949

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⁾).

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