Speaker: Marcello
Aguiar,
Texas A&M
Title:
Noncommutative symmetric
functions and related Hopf algebras
Abstract:
We start by recalling the construction of the descent algebra of
Solomon. This is a subalgebra of the symmetric group algebra
with ties to free Lie algebras on one hand and to the
representation theory of the symmetric group on the other.
Next we enlarge the picture to include noncommutative and
commutative symmetric functions. We give a brief overview of the
significance of the Hopf algebra structure of these objects from
the point of view of representation theory.
We then discuss the construction of a closely related Hopf algebra of
permutations through SchurWeyl duality and the convolution of
endomorphisms, due to Malvenuto and Reutenauer.
Finally, we mention some generalizations involving other dualities or
other products of endomorphisms, which is the subject of work in
progress.
