2 problems

Lam's conjecture. The cylindric Schur function $K_{(P,O)}(x_1,x_2,\ldots)$ is a positive linear combination of affine Schur functions, or equivalently dual $k$-Schur functions.

Let $\tilde{S}_n$ be the affine symmetric group, and let $\tilde{F}_w(X)$ denote the affine Stanley symmetric function associated with $w\in\tilde{S}_n$. For a Grassmannian affine…