4 problems

Kac–Moody extension conjecture. The analogues of the equations giving the Chevalley formulae for $\lambda$ and $-\lambda$ hold for $W$.

New-variable sign conjecture. The coefficients of the $s_i,\delta$-monomials in the $\mathbf{[w]}$-expansion of the $\mC[p]$ classes have sign $(-1)^{\ell(w)}$.

Let $G/B$ be a flag variety with Weyl group $W$, Schubert cells $X(w)^\circ$, and coefficients $c(w;u)$ in the Schubert expansion … Let $\leq$ denote the Bruhat order. Nonvanishing…

Let $G/B$ be a flag variety with Weyl group $W$, positive simple roots $alpha_1,\ldots,\alpha_r$, and Schubert cells $X(w)^\circ$. Write the motivic Chern class in the Schubert bas…