Abstract
In this paper, we give the decomposition into irreducible characters of the restriction to the wreath product of any irreducible character of
where p is any odd prime,
is an integer, and
and
denote the cyclic groups of order p and p – 1 respectively. This answers the question of how to decompose the restrictions to p-regular elements of irreducible characters of the symmetric group
in the
-basis corresponding to the p-basic set of
described previously by Brunat and Gramain. The result is given in terms of the Littlewood-Richardson coefficients for the symmetric group.
Communicated by J. Zhang
2010 Mathematics Subject Classification: