The center conjecture for non-semisimple BMW algebras

Let Bn(q,t)B_n(q,t) be the Birman–Murakami–Wenzl algebra over C\mathbb{C}, and let WL[x1,,xn]WL[x_1,\ldots,x_n] denote the commutative central subalgebra generated by the elements x1,,xnx_1,\ldots,x_n. Assume that qCq\in\mathbb{C} is generic, t=q2at=q^{2a}, and Bn(q,t)B_n(q,t) is non-semisimple.

Center conjecture. The center of Bn(q,q2a)B_n(q,q^{2a}) is

Z(Bn(q,q2a))=WL[x1,,xn].Z(B_n(q,q^{2a}))=WL[x_1,\ldots,x_n].

This would identify the explicitly constructed commutative subalgebra with the full center in the non-semisimple setting, extending the role of the Jucys–Murphy-type elements in separating blocks. The source does not state a resolution of the conjecture.

Sources & referencesView supporting material

Primary source

Christoforos Milionis, “The center of the BMW algebras and an Okounkov-Vershik like approach”, arXiv:2512.17458 (2026).

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