Affine geometric crystals in unipotent loop groups

DOI10.1090/S1088-4165-2011-00410-6zbMath1250.17026arXiv1004.2233MaRDI QIDQ2889341

Pavlo Pylyavskyy, Thomas Lam

Publication date: 7 June 2012

Published in: Representation Theory of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.2233

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) Loop groups and related constructions, group-theoretic treatment (22E67)

Related Items

Toric networks, geometric \(R\)-matrices and generalized discrete Toda lattices, Crystals and total positivity on orientable surfaces, Kirillov-Reshetikhin crystals \(B^{1, s}\) for \(\widehat{\mathfrak{s}\mathfrak{l}}_n\) using Nakajima monomials, Total positivity in loop groups. I: Whirls and curls, Geometric lifting of the integrable cellular automata with periodic boundary conditions, Differential equations for the closed geometric crystal chains

Cites Work

• Total positivity in loop groups. I: Whirls and curls
• Intrinsic energy is a loop Schur function
• Tropical R maps and affine geometric crystals
• Affine geometric crystals and limit of perfect crystals
• AFFINE CRYSTALS AND VERTEX MODELS
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