4 problems

Let $\mathcal P(r)$ be the polynomial space in which the stable atoms form a basis, and let stable atom positivity mean that the coefficients in this basis belong to…

Positive key expansion conjecture.

Let $\alpha\in\mathbb Z_{\geq0}^n$, and let $E_\alpha(X;q,t)$ be the nonsymmetric Macdonald polynomial. Write … where $<_S$ is the ordering generated by the stated transposition an…

Cherednik–Orr conjecture. Assume that $\la$ is an antidominant weight. Then