International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1365-1379
Character theory of infinite wreath products
Department of Mathematics, Drexel University, Philadelphia 19104, PA, USA
Received 31 August 2003; Revised 19 March 2005
Copyright © 2005 Robert Boyer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 -invariant of the group
-algebra is also determined.