Let U_epsilon(g) be the simply connected quantized enveloping algebra at roots of one associated to a finite dimensional complex simple Lie algebra g. The De Concini-Kac Procesi conjecture on the dimension of the irreducible representations of U_epsilon(g) is proved for the representations corresponding to the spherical conjugacy classes of the simply connected algebraic group G with Lie algebra 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.
Spherical orbits and representations of U_e(g)
CANTARINI, NICOLETTA;CARNOVALE, GIOVANNA;COSTANTINI, MAURO
2005
Abstract
Let U_epsilon(g) be the simply connected quantized enveloping algebra at roots of one associated to a finite dimensional complex simple Lie algebra g. The De Concini-Kac Procesi conjecture on the dimension of the irreducible representations of U_epsilon(g) is proved for the representations corresponding to the spherical conjugacy classes of the simply connected algebraic group G with Lie algebra 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.File in questo prodotto:
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