Grassmannian-parameterized solutions to direct-sum polygon and simplex equations
Mathematical Physics
2021-05-04 v4 math.MP
Quantum Algebra
Abstract
We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang--Baxter (2-simplex), respectively. We examine the general structure of (2n+1)-gon and 2n-simplex equations in direct sums of vector spaces. Then we provide a construction for their solutions, parameterized by elements of the Grassmannian Gr(n+1,2n+1).
Cite
@article{arxiv.2009.02352,
title = {Grassmannian-parameterized solutions to direct-sum polygon and simplex equations},
author = {Aristophanes Dimakis and Igor Korepanov},
journal= {arXiv preprint arXiv:2009.02352},
year = {2021}
}
Comments
26 pages, 5 tikz figures. v4: Introduction re-written, Discussion added in the end