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arXiv · 1708.08445

Totally positive matrices and dilogarithm identities

Andrei Bytsko·Alexander Volkov
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Abstract

We show that two involutions on the variety $N_n^+$ of upper triangular totally positive matrices are related, on the one hand, to the tetrahedron equation and, on the other hand, to the action of the symmetric group $S_3$ on some subvariety of $N_n^+$ and on the set of certain functions on $N_n^+$. Using these involutions, we obtain a family of dilogarithm identities involving minors of totally positive matrices. These identities admit a form manifestly invariant under the action of the symmetric group $S_3$.

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BibTeXRIS

Andrei Bytsko, Alexander Volkov. 2017-08-26. Totally positive matrices and dilogarithm identities. https://arxiv.org/abs/1708.08445

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