2024/11/18 by Maxim Kazarian, Kazarian, Maxim, Zhuoke Yang +1
Computer Science · #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2411.11546
openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \mathfrakso(N), \mathfraksp(2M), as well as Lie superalgebras \mathfrakosp(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 \mathfrakgl(N) and superalgebras \mathfrakgl(N|M) introduced earlier by the second named author.