# Moscow Mathematical Journal

Volume 24, Issue 2, April–June 2024 pp. 201–217.

Algebras of Conjugacy Classes in Symmetric Groups and Checker Triangulated Surfaces

**Authors**:
Yu. A. Neretin (1)

**Author institution:**(1) Math. Dept., University of Vienna,
Oskar-Morgenstern-Platz 1, 1090 Wien;

Institute for Information Transmission Problems;

Institute for Theoretical and Experimental Physics (until 11.2021);

Mech. Math. Dept., Moscow State University

**Summary: **

In 1999 V. Ivanov and S. Kerov observed that structure constants of algebras of conjugacy classes of symmetric groups $S_n$ admit a stabilization (in a non-obvious sense) as $n\to \infty$. We extend their construction to a class of pairs of groups $G\supset K$ and algebras of conjugacy classes of $G$ with respect to $K$. In our basic example, $G=S_n \times S_n$, $K$ is the diagonal subgroup $S_n$. In this case we get a geometric description of this algebra.

2020 Math. Subj. Class. 20B30, 20C32, 20E45.

**Keywords:**Symmetric groups, group algebras, Ivanov–Kerov algebra, partial bijections, triangulated surfaces, conjugacy classes.

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