2022/02/02 by Ma, Ying, Shoji, Toshiaki, Zhou, Zhiping
#17B37 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2202.00844
Let \mathbf Uq- be the negative part of the quantum enveloping algebra, and σ the algebra automorphism on \mathbf Uq- induced from a diagram automorphism. Let \underline\mathbf Uq- be the quantum algebra obtained from σ, and \widetilde\mathbf B (resp. \widetilde\underline\mathbf B) the canonical signed basis of \mathbf Uq- (resp. \underline\mathbf Uq-). Assume that \mathbf Uq- is simply-laced of finite or affine type. In our previous papers [SZ1, 2], we have proved by an elementary method, that there exists a natural bijection \widetilde\mathbf Bσ ≃ \widetilde\underline\mathbf B in the case where σ is admissible. In this paper, we show that such a bijection exists even if σ is not admissible, possibly except some small rank cases.