Universal Polynomial $\mathfrak{so}$ Weight System
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912123220656128 |
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| author | Kazarian, Maxim Yang, Zhuoke |
| author_facet | Kazarian, Maxim Yang, Zhuoke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal Polynomial $\mathfrak{so}$ Weight System Kazarian, Maxim Yang, Zhuoke Combinatorics 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. |
| title | Universal Polynomial $\mathfrak{so}$ Weight System |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.11546 |