3 problems

Equality conjecture. For $n\geq2$, $0<a\leq n$, $1\leq k\leq n-1$, and $\max\{0,a-n+k\}<s\leq\min\{a,k\}$,

Let $G$ be a connected reductive group over $k$, let $T$ be a maximal torus, let $W$ be its Weyl group, and fix a Weyl chamber. Let $\vec\rho$ be half the sum of the positive roots…

Let $M$ be the $d$-dimensional space equipped with an arbitrary $sigma$-semilinear operator $\sigma_M$, and let $\mathcal{X}_{\leqslant e}(\sigma_M)$, $\mathcal{X}_{\mu}(\sigma_M)$…