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- W2975831619 abstract "We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X otimes V^{otimes k})$ for Orthogonal and Symplectic groups. Thus we obtain a compact analogue of Schur-Weyl duality. We study functors $F_{mu,k}$ from the category of admissible $O(p,q)$ or $Sp_{2n}(mathbb{R})$ modules to representations of the type B/C affine Brauer algebra $mathfrak{B}_k^theta$. Thus providing a Akawaka-Suzuki-esque link between $O(p,q)$ (or $Sp_{2n}(mathbb{R})$) and $mathfrak{B}_k^theta$. Furthermore these functors take non spherical principal series modules to principal series modules for the graded Hecke algebra of type $D_k$, $C_{n-k}$ or $B_{n-k}$. With this we get a functorial correspondence between admissible simple $O(p,q)$ (or $Sp_{2n}(mathbb{R})$) modules and graded Hecke algebra modules." @default.
- W2975831619 created "2019-10-03" @default.
- W2975831619 creator A5003490817 @default.
- W2975831619 date "2019-09-25" @default.
- W2975831619 modified "2023-10-15" @default.
- W2975831619 title "Compact Schur-Weyl duality and the affine Type B/C Brauer algebra" @default.
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