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.