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A Pieri rule for key polynomials

Danjoseph Quijada
Wednesday, December 4, 2019 - 3:30pm to 5:00pm
PDL C-401
Danjoseph Quijada

The Pieri rule for the product of a Schur function and a single row Schur function is notable for having an elegant bijective proof that can be intuited by the rule’s concise diagrammatic interpretation, to wit, by appending cells to a Young diagram. Now, key polynomials generalize Schur polynomials to a basis of the full polynomial ring, in which they also refine the Schubert basis via a nice formula. In this talk, I will describe a Pieri rule for the product of a key polynomial and a single row key polynomial that can be analogously interpreted as appending cells to a key diagram, albeit potentially dropping some cells in between each cell addition. I will also outline the main points of the rule’s bijective proof, and in the process hopefully illustrate the utility of understanding the rule from a diagrammatic perspective. Joint work with Sami Assaf.