Algebras of conjugacy classes in symmetric groups

Abstract

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 $G$ is a product of symmetric groups, $G=S_n\times S_n$, $K$ is the diagonal subgroup $S_n$.

19p., 6 fig, extended version

References in corpus (3)

• Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument
• Asymptotic Hurwitz numbers
• Partial isomorphisms over finite fields

Cited by in corpus (1)

• Symmetric groups and checker triangulated surfaces