Combinatorial \(R\) matrices for a family of crystals: \(B_n^{(1)}\), \(D_n^{(1)}\), \(A_{2n}^{(2)}\) and \(D_{n+1}^{(2)}\) cases

DOI10.1006/jabr.2001.9017zbMath1020.17010arXivmath/0012247OpenAlexW1973163430MaRDI QIDQ1348680

Taichiro Takagi, Goro Hatayama, Masato Okado, Atsuo Kuniba

Publication date: 1 October 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0012247

zbMATH Keywords

tableauxquantum affine algebracombinatorial \(R\) matrixcrystal basisinsertion algorithmRobinson-Schensted correspondenceaffine crystalinhomogeneous case

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (6)

Scattering rule in soliton cellular automaton associated with crystal base of Uq(D4(3)) ⋮ Lusztig's \(q\)-analogue of weight multiplicity and one-dimensional sums for affine root systems ⋮ Branching rules, Kostka-Foulkes polynomials and \(q\)-multiplicities in tensor product for the root systems \(B_n\), \(C_n\) and \(D_n\) ⋮ Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection ⋮ Soliton cellular automaton associated with $D_n^{(1)}$Dn(1)-crystal B2,s ⋮ Analysis of a particle antiparticle description of a soliton cellular automaton

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Orthogonal tableaux and an insertion algorithm for \(SO(2n+1)\)
• A Schensted-type correspondence for the symplectic group
• The Bethe Ansatz and the combinatorics of Young tableaux
• Kostka polynomials and energy functions in solvable lattice models
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Schensted-type correspondence, plactic monoid, and jeu de taquin for type \(C_n\)
• Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varieties
• Inhomogeneous lattice paths, generalized Kostka polynomials and \(A_{n-1}\) supernomials
• COMBINATORICS OF CRYSTALS FOR TENSOR AND SPINOR REPRESENTATIONS OF U_q(B_n)
• Longest Increasing and Decreasing Subsequences
• A Schensted Algorithm Which Models Tensor Representations of the Orthogonal Group
• AFFINE CRYSTALS AND VERTEX MODELS

This page was built for publication: Combinatorial \(R\) matrices for a family of crystals: \(B_n^{(1)}\), \(D_n^{(1)}\), \(A_{2n}^{(2)}\) and \(D_{n+1}^{(2)}\) cases