Hats, ribbons and HallLittlewood symmetric functionsMike ZabrockiUniversity of Quebec at Montreal
April 7,

ABSTRACT


An operator on symmetric functions was introduced by Jing that adds a row to the partition indexing a HallLittlewood symmetric function. The action of this operator on the Schur basis is a of qanalog of the Pieri rule and can be used to calculate Schur function expansions of the HallLittlewood polynomials. We consider instead the recursion for building the HallLittlewood symmetric functions by adding columns. We constuct operators that have a very combinatorial action on the Schur function basis and give a new and elegant recurrence for building the HallLittlewood symmetric functions from smaller ones. The main tool that we use is simple and suprising involution on the space of operators that exchanges the unit for the counit in the Hopf algebra structure of this space. When the involution is applied to our combinatorial operators, the effect is that it permutes them in a very natural manner. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

