Auslander–Reiten quiver and representation theories related to KLR-type Schur–Weyl duality
Copyright policy )Auslander–Reiten quiver and representation theories related to KLR-type Schur–Weyl duality
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 $U_q(E_{6,7,8}^{(1)})$.
To be appeared in Mathematische Zeitschrift
- Ewha Womans University Korea (Republic of)
positive roots, distance polynomial, Connections of Hopf algebras with combinatorics, Auslander-Reiten quiver, \([Q]\)-distance, KLR algebra, exceptional E-types, Quantum groups (quantized enveloping algebras) and related deformations, \([Q]\)-socle, generalized KLR-type Schur-Weyl duality, 05E10, 16T30, 17B37, 81R50, Combinatorial aspects of representation theory, convex orders, FOS: Mathematics, Representations of quivers and partially ordered sets, Mathematics - Combinatorics, Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory
positive roots, distance polynomial, Connections of Hopf algebras with combinatorics, Auslander-Reiten quiver, \([Q]\)-distance, KLR algebra, exceptional E-types, Quantum groups (quantized enveloping algebras) and related deformations, \([Q]\)-socle, generalized KLR-type Schur-Weyl duality, 05E10, 16T30, 17B37, 81R50, Combinatorial aspects of representation theory, convex orders, FOS: Mathematics, Representations of quivers and partially ordered sets, Mathematics - Combinatorics, Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory
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