Level 1 perfect crystals and path realizations of basic representations at q = 0

DOI10.1155/IMRN/2006/10312zbMath1149.17016arXivmath/0507114OpenAlexW2039901562MaRDI QIDQ3428132

Hyeonmi Lee, Igor B. Frenkel, Seok-Jin Kang, Georgia M. Benkart

Publication date: 27 March 2007

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507114

zbMATH Keywords

energy functionaffine Lie algebracrystalpath realization

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (19)

Level 0 Monomial Crystals ⋮ Kirillov-Reshetikhin crystals for nonexceptional types ⋮ Littelmann paths for the basic representation of an affine Lie algebra ⋮ Young wall model for A₂⁽²⁾-type adjoint crystals ⋮ Categorical relations between Langlands dual quantum affine algebras: exceptional cases ⋮ Affine structures and a tableau model for \(E_{6}\) crystals ⋮ Uniform description of the rigged configuration bijection ⋮ A crystal to rigged configuration bijection and the filling map for type \(D_4^{(3)}\) ⋮ Combinatorial structure of Kirillov-Reshetikhin crystals of type \(D_n^{(1)}\), \(B_n^{(1)}\), \(A^{(2)}_{2n-1}\) ⋮ A uniform approach to soliton cellular automata using rigged configurations ⋮ Existence of crystal bases for Kirillov-Reshetikhin modules of type \(D\) ⋮ Perfect crystals for \(U_q(D_4^{(3)})\) ⋮ Quiver Varieties and Adjoint Crystals of Level ℓ for TypeA_n⁽¹⁾ ⋮ On the connection between Young walls and Littelmann paths ⋮ Adjoint crystals and Young walls for \(U_q(\widehat{sl}_2)\) ⋮ A generalization of adjoint crystals for the quantized affine algebras of type \(A^{(1)}_n\), \(C^{(1)}_n\) and \(D^{(2)}_{n+1}\) ⋮ On Demazure crystals for $U_{q}(G_{2}^{(1)})$ ⋮ Existence of Kirillov–Reshetikhin crystals for nonexceptional types ⋮ Quiver varieties and path realizations arising from adjoint crystals of type 𝐴_{𝑛}⁽¹⁾

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