ALGEBRAS OF CONJUGACY CLASSES IN SYMMETRIC GROUPS AND CHECKER TRIANGULATED SURFACES

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