Degree of Parabolic Quantum Groups - Dipartimento di Matematica ...

1. Poisson algebraic Groups 18
Finally, consider the map µ : G ∗ → G given by µ((b1, b2)) = b −1
1 b2,
so that µ is a covering of the big Bruhat cell B − B + . De Concini, Kaç and
Procesi shows in [DCKP92], that as soon as C ⊂ G is a conjugacy class, until
dimC > 0, µ −1 (C) ⊂ G ∗ is a single symplectic leaf of G ∗ . If dimC = 0, i.e.
C = {x} is an element of the center of G, then µ −1 (x) has a finite number
of elements each of which is a symplectic leaf.