Algebras of conjugacy classes in symmetric groups

Yury A. Neretin

Published 2016-04-19Version 1

In 1999 V. Ivanov and S. Kerov observed that structure constants of algebras of conjugacy classes of symmetric groups $S_n$ admit a stabiluzation (in a nontrivial sence) as $n\to \infty$. We extend their construction to a certain class of pairs of groups $G\supset K$ and algebras of conjugacy classes of $G$ with respect to $K$ (as $S_{kn}\supset S_n$, $S_n\times S_n \supset S_n$, etc.).