Kohnert Properties of Northeast Diagrams

Alexander Moon
Graduate Student
University of Wisconsin – Milwaukee

Kohnert polynomials and posets are combinatorial objects with deep representation theoretic meaning, generalizing both Schubert polynomials and Demazure characters, i.e., key polynomials. In this talk I will explore what Kohnert posets and polynomials are in general, then I will discuss some recent results centering on the Kohnert properties of “northeast” diagrams. I will present some conditions for the boundedness and rankedness of a “northeast” Kohnert poset and present a surprising connection between certain minimal elements and key diagrams. There will be a worksheet. This is a joint work with Aram Bingham, Beth Anne Castellano, Kimberly Hadaway, Reuven Hodges, Yichen Ma, and Kyle Salois that originated at this year’s GRWC.