Nicolás Libedinsky

Polytopal invariance for Lusztig's $q$-weight multiplicities

Let $\Phi$ be an irreducible root system normalized so that long roots have length $\sqrt{2}$, and let $\mu\leq\lambda$ be dominant weights. We associate to $(\Phi,\mu,\lambda)$ the convex polytope $$P^{\Phi}_{\mu,\lambda} = (\mu+C)\cap(\lambda-C)\cap(\overline{D}-\rho),$$ where $C=\mathbb{R}_{\geq 0}\Phi^+$ and $\over...