Block representation type of reduced enveloping algebras

Abstract

Let K K be an algebraically closed field of characteristic p p , G G a connected, reductive K K -group, g = Lie ( G ) \mathfrak {g}=\text {Lie}(G) , χ ∈ g ∗ \chi \in \mathfrak {g}^* and U χ ( g ) U_\chi (\mathfrak {g}) the reduced enveloping algebra of g \mathfrak {g} associated with χ \chi . Assume that G ( 1 ) G^{(1)} is simply-connected, p p is good for G G and g \mathfrak {g} has a non-degenerate G G -invariant bilinear form. All blocks of U χ ( g ) U_\chi (\mathfrak {g}) having finite and tame representation type are determined.