论文题目：Affine Brauer category and parabolic category O in types B, C, D

论文作者：Hebing Rui, Linliang Song

发表刊物：Mathematische Zeitschrift

成果介绍：

oA strict monoidal category referred to as affine Brauer category AB is introduced over a commutative ring κ containing multiplicative identity 1 and invertible element 2. We prove that morphism spaces in AB are free over κ. The cyclotmic (or level k) Brauer category CBf(ω) is a quotient category of AB. We prove that any morphism space in CBf(ω) is free over κ with maximal rank if and only if the u-admissible condition holds in the sense of (1.32). Affine Nazarov–Wenzl algebras (Nazarov in J Algebra 182(3):664–693, 1996) and cyclotomic Nazarov–Wenzl algebras (Ariki et al. in Nagoya Math J 182:47–134, 2006) will be realized as certain endomorphism algebras in AB and CBf(ω),respectively. We will establish higher Schur–Weyl duality between cyclotomic Nazarov–Wenzl algebras and parabolic BGG categories O associated to symplectic and orthogonal Lie algebras over the complex field C. This enables us to use standard arguments in (Anderson et al. in Pac J Math 292(1):21–59, 2018; Rui and Song in Math Zeit 280(3–4):669–689, 2015; Rui and Song in J Algebra 444:246–271, 2015), to compute decomposition matrices of cyclotomic Nazarov–Wenzl algebras. The level two case was considered by Ehrig and Stroppel in (Adv. Math. 331:58–142, 2018).

所属学科：基础数学

论文地址：http://link.springer.com/article/10.1007/s00209-018-2207-x