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arXiv · 2512.17458

The center of the BMW algebras and an Okounkov-Vershik like approach

Christoforos Milionis
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Abstract

We use the Jucys-Murphy elements of the BMW algebra to show that its center over the complex numbers for almost all parameters making it semisimple is given by Wheel Laurent polynomials, a subalgebra of the symmetric Laurent polynomials in the JM elements. As an application, we give an Okounkov-Vershik like approach to its finite dimensional representations. In the non semisimple case related to the type B Lie algebras, the central subalgebra of Wheel Laurent polynomials is large enough to separate blocks of the BMW algebras.

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BibTeXRIS

Christoforos Milionis. 2025-12-19. The center of the BMW algebras and an Okounkov-Vershik like approach. https://arxiv.org/abs/2512.17458

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