A bijection between type \(D_n^{(1)}\) crystals and rigged configurations
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Publication:1770478
DOI10.1016/j.jalgebra.2004.12.010zbMath1142.17304arXivmath/0406248OpenAlexW2055881321MaRDI QIDQ1770478
Publication date: 7 April 2005
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0406248
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Applications of Lie (super)algebras to physics, etc. (17B81) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Exactly solvable models; Bethe ansatz (82B23)
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Level 0 Monomial Crystals ⋮ \(X=M\) for symmetric powers ⋮ Connecting marginally large tableaux and rigged configurations via crystals ⋮ New fermionic formula for unrestricted Kostka polynomials ⋮ Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas ⋮ Rigged configurations and the \(\ast\)-involution ⋮ Type \(D_n^{(1)}\) rigged configuration bijection ⋮ Uniform description of the rigged configuration bijection ⋮ Crystal energy functions via the charge in types \(A\) and \(C\) ⋮ A crystal to rigged configuration bijection and the filling map for type \(D_4^{(3)}\) ⋮ Affine crystal structure on rigged configurations of type \(D_{n}^{(1)}\) ⋮ Stable rigged configurations for quantum affine algebras of nonexceptional types ⋮ Fusion products of Kirillov-Reshetikhin modules and the \(X = M\) conjecture ⋮ From Macdonald polynomials to a charge statistic beyond type \(A\) ⋮ Using rigged configurations to model \(B(\infty)\) ⋮ Rigged configurations for all symmetrizable types ⋮ Crystals and coboundary categories ⋮ Finite-dimensional crystals \(B^{2,s}\) for quantum affine algebras of type \(D^{(1)}_{n}\) ⋮ Rigged configuration bijection and proof of the \(X = M\) conjecture for nonexceptional affine types ⋮ Identities from representation theory ⋮ Crystal structure on rigged configurations and the filling map
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