2025/10/28 by Jang, Il-Seung, Kwon, Jae-Hoon, Uruno, Akito
#17B10 #17B37 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2510.24451
We construct a crystal base of the negative half of a quantum orthosymplectic superalgebra. It can be viewed as a limit of the crystal bases of q-deformed irreducible oscillator representations. We also give a combinatorial description of the embedding from the crystal of a q-oscillator representation to that of the negative half subalgebra given in terms of a PBW type basis. It is given as a composition of embeddings into the crystals of intermediate parabolic Verma modules, where the most non-trivial one is from an oscillator module to a maximally parabolic Verma module with respect to a quantum subsuperalgebra for \mathfrakglm|n. A new crystal theoretic realization of Burge correspondence of orthosymplectic type plays an important role for the description of this embedding.