2025/04/16 by Heo, Taehyeok
#05E10 #17B10 #17B37 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2504.12106
We define new crystal maps on B(∞) using its polyhedral realization, and show that the crystal B(∞) equipped with the new crystal maps is isomorphic to Kashiwara's B(∞) as bicrystals. In addition, we combinatorially describe the bicrystal structure of B(∞), which is called a sliding diamond rule. Using the bicrystal structure on B(∞), we define the extended crystal and show that it is isomorphic to the extended crystal introduced by Kashiwara and Park.