On sheets of orbit covers for classical semisimple lie groups
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David Vogan gave programmatic conjectures about the Dixmier’s map and he made two conjectures that induction may be independent of the choice of parabolic group used and the sheets of orbit data are conjugated or disjointed. In our previous paper, we gave a geometric version of the parabolic induction of the geometric orbit datum (i.e. orbit covers), and proved Vogan’s first conjecture for geometric orbit datum: the parabolic induction of the geometric orbit datum is independent of the choice of parabolic group. In this paper, we will prove the other Vogan’s conjecture, that is, the sheets are conjugated or disjointed for classical semisimple complex groups.
KeywordsLie group representation of Lie group Dixmier’s map geometric orbit data
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