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Permanent versus determinant, obstructions, and Kronecker coefficients
Citation key B-Permanent-Versus-Determinant-Obstructions-And-Kronecker-Coefficients
Author Peter Bürgisser
Year 2016
Journal Séminaire Lotharingien de Combinatoire
Volume 75
Month 05
Abstract We give an introduction to some of the recent ideas that go under the name ``geometric complexity theory''. We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent. We then introduce the concept of a representation theoretic obstruction, which has close links to algebraic combinatorics, and we explain some of the insights gained so far. In particular, we address very recent insights on the complexity of testing the positivity of Kronecker coefficients. We also briefly discuss the related asymptotic version of this question.
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