Quantum \mathfrakgl-weight system and its average values

2025/06/21 by Zaitsev, Mikhail
#05E05 #17B37 #20C08 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2506.17706

Abstract

We present a proof of a recent conjecture due to M. Kazarian, E. Krasilnikov, S. Lando, and M. Shapiro, which describes the average value of the universal \mathfrakgl-weight system on permutations. The proof uses a quantum analogue of the \mathfrakgl-weight system on Hecke algebras of type A, which leads to a one-parameter deformation of the average value of the universal \mathfrakgl-weight system. We show that the average value of the quantum weight system is a linear combination of one-part Schur functions, with coefficients being q-analogues of Bernoulli polynomials.

Citations

• Generalized chord diagrams and weight systems
• Generalized Harish-Chandra morphism on Reflection Equation algebras
• Weight systems and invariants of graphs and embedded graphs
• The GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization

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