Assembling crystals of type A

2012/12/23 by В. И. Данилов, Danilov, Vladimir I., Alexander V. Karzanov +3
Mathematics · #05C75 #05E99 #17B37 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1212.5771

openalex publication_date 2012/12/23 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28

Abstract

Regular A_n-crystals are certain edge-colored directed graphs which are related to representations of the quantized universal enveloping algebra U_q(\mathfraksl_n+1). For such a crystal K with colors 1,2,...,n, we consider its maximal connected subcrystals with colors 1,...,n-1 and with colors 2,...,n and characterize the interlacing structure for all pairs of these subcrystals. This is used to give a recursive description of the combinatorial structure of K and develop an efficient procedure of assembling K.

Related

• On the combinatorial structure of crystals of types A,B,C
• B₂-crystals: axioms, structure, models
• On the structure of regular B₂-type crystals
• Polyhedral realizations for B(∞) and extended Young diagrams, Young walls of type \rm A⁽¹⁾_n-1, \rm C⁽¹⁾_n-1, \rm A⁽²⁾_2n-2, \rm D⁽²⁾_n
• Higher level affine crystals and Young walls