Spherical orbits and representations of $U

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67852Let $U_ε(\mathfrak g)$ be the simply connected quantized enveloping algebra associated to a finite-dimensional complex simple Lie algebra $\mathfrak g$ at the roots of unity. The De Concini-Kac-Procesi conjecture on the dimension of the irreducible representations of $U_ε(\mathfrak g)$ is proved for representations corresponding to the spherical conjugacy classes of the simply connected algebraic group $G$ with Lie algebra $\mathfrak g$. We achieve this result by means of a new characterization of the spherical conjugacy classes of $G$ in terms of elements of the Weyl group.This new version includes part I and part II. Some typos are corrected and some remarks are addedQuantum AlgebraRepresentation Theory17B37 (primary), 17B10 (secondary)Spherical orbits and representations of $U_ε(\mathfrak g)$text