Representation Theory of Wreath Product with Symmetric Top Group

[FriedrichRober]

I think that knowing the territory decomposition for conjugacy classes of wreath products with a symmetric top group maybe could be useful for doing representation theory with such groups.

Say G = K wr H where H is a symmetric group of degree m and K has r conjugacy classes with representatives k_1, ..., k_r. Then we would store for each conjugacy class a matrix P of size r x m where the entry P_{i,j} encodes the number of wreath cycles with load (k_i, j).

[FriedrichRober]

This paper shows how one can construct all irreducible representations of such wreath products:

On the Eigenvalues of Representations of Reflection Groups