Student Combinatorics and Algebra Seminar


Abstract 

Schur polynomials can be written as a sum of Demazure atoms, which are certain polynomials indexed by elements of the symmetric group. Similarly, symmetric Grothendieck polynomials can be decomposed into Lascoux atoms, though these atoms are as yet a bit more mysterious. In this talk, we will explore the motivating Schur case via combinatorial, representation theoretic, geometric, and lattice model perspectives; define Lascoux atoms and describe how they can be realized as the partition function of a certain colored lattice model; give some consequences of this realization; and discuss future research ideas. Based on joint work with Valentin Buciumas and Travis Scrimshaw. 