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The maximal dimensions of simple modules over restricted Lie algebras

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If you have a question about this talk, please contact Chris Parker.

Restricted Lie algebras were introduced by Jacobson in the 1940’s and ever since the first investigations into their representation theory, it has been understood that the simple modules of a given such algebra have bounded dimensions. In 1971 Kac and Weisfeiler made a striking conjecture (KW1) giving a precise formula for the maximal dimension M(g) of a restricted Lie algebra g.

In this talk I will give a general overview of this theory, and then I will describe a joint work with Ben Martin and David Stewart in which we apply the Leftschetz principle, along with classical techniques from Lie theory, to prove the KW1 conjecture for all restricted Lie subalgebras of the general linear algebra gl_n, provided the characteristic of the field is large compared to n.

This talk is part of the Algebra seminar series.

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