B₂-crystals: axioms, structure, models

2007/08/16 by V. I. Danilov, В. И. Данилов, A. V. Karzanov +5 · 4 citations
Chemistry · Mathematics · Physics and Astronomy · #05C75 #05E99 #17B37 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Axiom #Chemistry #Combinatorics #Combinatorics (math.CO) #Computer science #Crystal (programming language) #Crystal structure #Crystallography #Discrete mathematics #FOS: Mathematics #Geometry #Integrable system #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:05C75 #msc:05E99 #msc:17B37

paper · pdf · doi:10.48550/arxiv.0708.2198

published in arXiv (Cornell University) (Cornell University) · 33 pages, 9 figures, this paper is updated version of published version in Journal of Combinatorial Theory, Series A Volume 116, Issue 2, February 2009, Pages 265-289

openalex publication_date 2007/08/16 · arxiv created 2020/01/08 · arxiv updated 2020/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a list of ``local'' axioms and an explicit combinatorial construction for the regular B₂-crystals (crystal graphs of highest weight integrable modules over U_q(sp₄)). Also a new combinatorial model for these crystals is developed.

Citations

• Crystalizing theq-analogue of universal enveloping algebras
• Paths and Root Operators in Representation Theory

Cited by

• Rigged Configurations for all Symmetrizable Types

Related

• On the structure of regular B₂-type crystals
• Crystal skeletons: Combinatorics and axioms
• On the combinatorial structure of crystals of types A,B,C
• Crystal bases and monomials for U_q(G₂)-modules
• A Combinatorial Model for Crystals of Kac-Moody Algebras