Vanishing of trace forms in low characteristics

Details Vanishing of trace forms in low characteristics Vanishing of trace forms in low characteristics

2007-12-21

arxiv.org/abs/0712.3764v4

Algebra & Number Theory, vol. 3, #5 (2009), 543-566

Mathematics

Representation Theory

Slightly revised since v3. Added short section 8 on Richardson's condition

Scientific paper

Every finite-dimensional representation of an algebraic group G gives a trace symmetric bilinear form on the Lie algebra of G. We give criteria in terms of root system data for the existence of a representation such that this form is nonzero or nondegenerate. As a corollary, we show that a Lie algebra of type E8 over a field of characteristic 5 does not have a so-called "quotient trace form", answering a question posed in the 1960s.

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