Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

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.