Relatives of the Symmetric Group Algebra.

Götz Pfeiffer, National University of Ireland, Galway

Friday May 19, 10.00-10.45, Groups in Galway 2006

Solomon's descent algebra and the Iwahori-Hecke algebra are both defined with respect to symmetric group: one is a subalgebra, the other a deformation of its group algebra. In fact, such algebras exist for every finite Coxeter group. They have been studied intensely, both as interesting objects in their own right, and because of their importance with applications in combinatorics and representation theory: the descent algebra occurs as the dual of the Hopf algebra of quasi-symmetric functions, the Iwahori-Hecke algebra as endomorphism ring of certain induced modules of finite groups of Lie type ... In this talk I will review some of their basic properties, present some new results (joint work with C. Bonnafe), and based on these discuss (the lack of) relationships between the two algebras.