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Spherical orbits and representations of $U_ε(\mathfrak g)$

Nicoletta Cantarini·Giovanna Carnovale·Mauro Costantini
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Abstract

Let $U_ε(\mathfrak g)$ 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.

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Nicoletta Cantarini, Giovanna Carnovale, Mauro Costantini. 2003-12-20. Spherical orbits and representations of $U_ε(\mathfrak g)$. https://arxiv.org/abs/math/0306321

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