Rank $n$ swapping algebra for Grassmannian

Abstract

The rank $n$ swapping algebra is the Poisson algebra defined on the ordered pairs of points on a circle using the linking numbers, where a subspace of $({\mathbb{K}}^n\times {\mathbb{K}}^{n\ast }{)}^r/\mathrm{GL}(n,\mathbb{K})$ is its geometric mode. In this paper, we find an injective Poisson homomorphism from the Poisson algebra on Grassmannian $G_{n,r}$ arising from boundary measurement map to the rank $n$ swapping fraction algebra.

13 pages, 5 figures. Improved version of arXiv:1503.00918v7 Section 5