Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :
Le 25 novembre 2004 à 13:45 -
Présentée par Aguiar Marcelo - Texas A&M University
The smash product of symmetric functions
We introduce a product on the space of symmetric
functions that interpolates between the classical "internal"
and "external" products (which are constructed in terms of tensor
products and induction of representations).
This product is best understood in terms of Hopf algebraic constructions
(the "smash product").
The smash product exists as well on the space of non-commutative
symmetric functions. At this level it interpolates between Solomon's
product (the "descent algebra") and the usual product of non-commutative
symmetric functions (as defined by Thibon et al).
The smash product also exists on larger spaces like the algebra of
Solomon-Tits and the algebra of Malvenuto-Reutenauer.
Familiarity with representation theory of the symmetric group
will be helpful but not strictly necessary to follow the talk.
This is joint work with Walter Ferrer and Walter Moreira.