Abstract
Let O be a nilpotent orbit of a complex semisimple Lie algebra g and let π:X→O¯ be the finite covering associated with the universal covering of O. In the previous article [14] we have explicitly constructed a Q-factorial terminalization X˜ of X when g is classical. In this article we count how many non-isomorphic Q-factorial terminalizations X has. We construct the universal Poisson deformation of X˜ over H2(X˜,C) and look at the action of the Weyl group W(X) on H2(X˜,C). The main result is an explicit geometric description of W(X).
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