4 papers
Grothendieck positivity for normal square root crystals
Eric Marberg, Kam Hung Tong, Tianyi Yu
Normal crystals (also known as Stembridge crystals) are commonly used to establish the Schur positivity of symmetric functions, as their characters are sums of Schur polynomials. I…
Ideal transition systems
Eric Marberg, Brendan Pawlowski
We study an inductive method of computing initial ideals and Gröbner bases for families of ideals in a polynomial ring. This method starts from a given set of pairs where $…
Crystals for set-valued decomposition tableaux
Eric Marberg, Kam Hung Tong
We describe two crystal structures on set-valued decomposition tableaux. These provide the first examples of interesting "-theoretic" crystals on shifted tableaux. Our first cry…
Primed decomposition tableaux and extended queer crystals
Eric Marberg, Kam Hung Tong
Our previous work introduced a category of extended queer crystals, whose connected normal objects have unique highest weight elements and characters that are Schur -polynomials…