论文题目: Affine Brauer category and parabolic category O in types B, C, D
论文作者: Hebing Rui, Linliang Song
oA strict monoidal category referred to as affine Brauer category is introduced over a commutative ring containing multiplicative identity 1 and invertible element 2. We prove that morphism spaces in are free over . The cyclotmic (or level k) Brauer category is a quotient category of . We prove that any morphism space in is free over with maximal rank if and only if the -admissible condition holds in the sense of (). Affine Nazarov–Wenzl algebras (Nazarov in J Algebra 182(3):664–693, ) and cyclotomic Nazarov–Wenzl algebras (Ariki et al. in Nagoya Math J 182:47–134, ) will be realized as certain endomorphism algebras in and , respectively. We will establish higher Schur–Weyl duality between cyclotomic Nazarov–Wenzl algebras and parabolic BGG categories associated to symplectic and orthogonal Lie algebras over the complex field . This enables us to use standard arguments in (Anderson et al. in Pac J Math 292(1):21–59, ; Rui and Song in Math Zeit 280(3–4):669–689, ; Rui and Song in J Algebra 444:246–271, ), 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, ).