International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1365-1379
doi:10.1155/IJMMS.2005.1365

Character theory of infinite wreath products.

Abstract

The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identification is called the “asymptotic character formula.” The K0-invariant of the group C∗-algebra is also determined.