$B_2$-crystals: axioms, structure, models
V. I. Danilov, A. V. Karzanov, G. A. Koshevoy
TL;DR
This paper introduces new local axioms and a combinatorial model for regular B2-crystals, which are graph structures representing certain algebraic modules over quantum groups, enhancing understanding and construction methods.
Contribution
It provides the first explicit combinatorial construction and a new model for B2-crystals, advancing the combinatorial representation theory of quantum groups.
Findings
List of local axioms for B2-crystals
Explicit combinatorial construction of B2-crystals
Development of a new combinatorial model for these crystals
Abstract
We present a list of ``local'' axioms and an explicit combinatorial construction for the regular -crystals (crystal graphs of highest weight integrable modules over ). Also a new combinatorial model for these crystals is developed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Nonlinear Waves and Solitons