Algebraic and Enumerative Combinatorics Seminar | Theta operators and LLT positivity

Abstract: I will introduce a family of commuting derivations on the ring of symmetric polynomials. Using this family I will then define an apparently-novel family of symmetric functions that is vertical-strip LLT positive and relates directly to the Theta operators of D'Adderio–Iraci–Vanden Wyngaerd. Finally I'll discuss some consequences for the "higher order" Macdonald positivity conjecture of Dołęga. This is joint work with Jim Haglund.

There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.