Let f be a nilpotent linear function on a complex simple Lie algebra g=Lie G
and d=(dim G f)/2. Let k be an algebraically closed field of characteristic p and g_k=Lie(G_k),
where G_k is a simple algebraic k-group of the same type as G.
We shall discuss a relationship between 1-dimensional representations of the finite W-algebra W(g,f),
representations of dimension p^d of the reduced enveloping algebra U_f(g_k) and
completely prime primitive ideals of U(g) whose associated variety equals the Zariski closure of Gf.

Lecture #12679

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