2021/11/14 by Kashiwara, Masaki, Park, Euiyong
#05E10 #17B37 #18D10 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2111.07255
A new categorical crystal structure for the quantum affine algebras is presented. We introduce the extended crystal \widehatB_\mathfrakg(∞) for an arbitrary quantum group, which is the product of infinite copies of the crystal B(∞). For a complete duality datum in the Hernandez-Leclerc category C0_\mathfrakg of a quantum affine algebra Uq'(\mathfrakg), we prove that the set of the isomorphism classes of simple modules in C0_\mathfrakg has an extended crystal structure isomorphic to the extended crystal \widehatB_\mathfrakg(∞). An explicit combinatorial description of the extended crystal \widehatB_\mathfrakg(∞) for affine type An(1) is given in terms of affine highest weights.