# im体育

（芮和兵、宋林亮）Affine Brauer category and  parabolic category  O  in types B, C, D

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 (). 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 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, ; 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, ).

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