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arXiv · 2411.11546

Universal Polynomial $\mathfrak{so}$ Weight System

Maxim Kazarian·Zhuoke Yang
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Abstract

We introduce a universal weight system (a function on chord diagrams satisfying the $4$-term relation) taking values in the ring of polynomials in infinitely many variables whose particular specializations are weight systems associated with the Lie algebras $\mathfrak{so}(N)$, $\mathfrak{sp}(2M)$, as well as Lie superalgebras $\mathfrak{osp}(N|2M)$. We extend this weight system to permutations and provide an efficient recursion for its computation. The construction for this weight system extends a similar construction for the universal polynomial weight system responsible for the Lie algebras $\mathfrak{gl}(N)$ and superalgebras $\mathfrak{gl}(N|M)$ introduced earlier by the second named author.

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Maxim Kazarian, Zhuoke Yang. 2024-11-18. Universal Polynomial $\mathfrak{so}$ Weight System. https://arxiv.org/abs/2411.11546

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