Nolan Wallach

Abstract:   The speaker calculated the minimal polynomial of the sum of all one card shuffles of a deck with n cards in the group algebra of the symmetric group on n letters in 1984. This result was used in the proof of a refinement of a theorem of Kostant and Lynch. In this lecture we will see how this identity plays a role in the speaker's recent joint work with Adriano Garsia that proves that the algebra of quasisymmetric polynomials in n indeterminates is is a free module over the subring of symmetric polynomials.