nLab positive Grassmannian

Definition

The totally nonnegative Grassmanian (informally called the positive Grassmannian) $G_+(n,k)$ is the part of the real Grassmannian $G(n,k)(\mathbf{R}^n)$ which consists of points for which all maximal minors are nonnegative.

Related entries

• Grassmannian

• total positivity

• amplituhedron

• positroid

References

• Alexander Postnikov, Lectures on positive Grassmannian, writeup by A. Morales [pdf]

• Lauren K. Williams, The positive Grassmannian, the amplituhedron, and cluster algebras [arXiv:2110.10856]

• Prashanth Raman: Lecture Notes on Positivity Properties of Scattering Amplitudes [arXiv:2603.28454]