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arXiv · 2412.14716

The center of the walled Brauer algebra $B_{r,1}(\delta)$

Eirini Chavli·Maud De Visscher·Alison Parker·Sarah Salmon·Ulrica Wilson
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Abstract

We show that the centre of the walled Brauer algebra $B_{r,1}(\delta)$ over the complex field $\mathbb{C}$, for any parameter $\delta\in \mathbb{C}$, is generated by the supersymmetric polynomials evaluated at the Jucys-Murphy elements. Moreover, we prove that its dimension is independent of the parameter $\delta$.

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Eirini Chavli, Maud De Visscher, Alison Parker, Sarah Salmon, Ulrica Wilson. 2024-12-19. The center of the walled Brauer algebra $B_{r,1}(\delta)$. https://arxiv.org/abs/2412.14716

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