Year: 2026
Type: preprint
Abstract: We introduce stable symmetric series which encode normalized conjugacy classes and their multiplication operators simultaneously for all symmetric groups. This gives a direct route from the Ivanov--Kerov algebra to shifted symmetric functions and to differential operators in $U(\mathcal W_{1+\infty})$. Using the Goulden--Jackson product, we extend the construction to Jack polynomials, recover shifted Jack eigenvalues and Pieri-type relations, and obtain explicit candidate operators in degrees three and four. Their real and quaternionic specializations to zonal polynomials are verified by Gaussian matrix integrals and exhaustive Wick enumeration.
Source: arXiv (Cornell University)
Author: Thibon, Jean-Yves
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204459562