Hats, ribbons and Hall-Littlewood symmetric functions

Mike Zabrocki

University of Quebec at Montreal

April 7,
refreshments at 3:45pm


An operator on symmetric functions was introduced by Jing that adds a row to the partition indexing a Hall-Littlewood symmetric function. The action of this operator on the Schur basis is a of q-analog of the Pieri rule and can be used to calculate Schur function expansions of the Hall-Littlewood polynomials.

We consider instead the recursion for building the Hall-Littlewood 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 Hall-Littlewood 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.

Speaker's Contact Info: zabrocki(at-sign)math.uqam.ca

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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