Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type \(D_n\)

DOI10.1007/s10801-007-0057-4zbMath1171.17004arXivmath/0603160OpenAlexW2111997256WikidataQ126266843 ScholiaQ126266843MaRDI QIDQ2457939

Tomoki Nakanishi, Wakako Nakai

Publication date: 24 October 2007

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603160

zbMATH Keywords

quantum groupYoung tableau\(q\)-characterlattice path

Mathematics Subject Classification ID

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

Related Items

Yangian Characters and Classical $$\mathcal{W}$$ -Algebras, Representations of quantum affine algebras of type $B_N$, Path description of type B \(q\)-characters, On multigraded generalizations of Kirillov-Reshetikhin modules

Cites Work

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• Binomial determinants, paths, and hook length formulae
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Young-diagrammatic methods for the representation theory of the classical groups of type \(B_ n\), \(C_ n\), \(D_ n\)
• Quantum affine algebras
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Analytic Bethe ansatz for fundamental representations of Yangians
• Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type \(C_n\)
• Characters of fundamental representations of quantum affine algebras.
• Finite-dimensional crystals \(B^{2,s}\) for quantum affine algebras of type \(D^{(1)}_{n}\)
• Paths, tableaux andq-characters of quantum affine algebras: theC_ncase
• The Kirillov-Reshetikhin conjecture and solutions of T-systems
• Restricted solid-on-solid models connected with simply laced algebras and conformal field theory
• Quantum Jacobi-Trudi and Giambelli formulae for U_q(B_r⁽¹⁾) from the analytic Bethe ansatz
• Virtual crystals and fermionic formulas of type 𝐷_{𝑛+1}⁽²⁾, 𝐴_{2𝑛}⁽²⁾, and 𝐶_{𝑛}⁽¹⁾
• Combinatorics of \(q\)-characters of finite-dimensional representations of quantum affine algebras.
• Lattice path proofs for determinantal formulas for symplectic and orthogonal characters