A survey of total positivity

Details A survey of total positivity A survey of total positivity

2007-05-25

arxiv.org/abs/0705.3842v1

Mathematics

Representation Theory

8 pages

Scientific paper

We survey the history of totally positive matrices and the generalization to Lie groups. We describe a reduction of a bilinear form to a canonical form (generalizing the case of symplectic nondegenerate forms) using ideas from total positivity; we also place this in a Lie group context. We give a short exposition of results of Fock and Goncharov on the study of homomorphisms of the fundamental group of a closed surface into a Lie group.

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