A new basis for idempotents in the descent algebra

Stephanie van Willigenburg
(Visiting York University)

Abs: We shall recall some details about symmetric functions, and define a certain set of minimal idempotents in the descent algebra of the symmetric group. From here we shall set up the problem I am working on at present, which concerns finding a new basis for these idempotents whose coefficients lie in the ring of symmetric functions. We shall then motivate why we should want to look for such a basis.