# Totally nonnegative cells and Matrix Poisson varieties

Goodearl, Ken, Launois, Stephane, Lenagan, T.H. (2011) Totally nonnegative cells and Matrix Poisson varieties. Advances in Mathematics, 226 (1). pp. 779-826. ISSN 0001-8708. (doi:10.1016/j.aim.2010.07.010) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:26019)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. Official URLhttp://dx.doi.org/10.1016/j.aim.2010.07.010

## Abstract

We describe explicitly the admissible families of minors for the totally nonnegative cells of real matrices, that is, the families of minors that produce nonempty cells in the cell decompositions of spaces of totally nonnegative matrices introduced by A. Postnikov. In order to do this, we relate the totally nonnegative cells to torus orbits of symplectic leaves of the Poisson varieties of complex matrices. In particular, we describe the minors that vanish on a torus orbit of symplectic leaves, we prove that such families of minors are exactly the admissible families, and we show that the nonempty totally nonnegative cells are the intersections of the torus orbits of symplectic leaves with the spaces of totally nonnegative matrices.

Item Type: Article 10.1016/j.aim.2010.07.010 Q Science > QA Mathematics (inc Computing science) > QA150 AlgebraQ Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Q Science > QA Mathematics (inc Computing science) > QA564 Algebraic Geometry Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Stephane Launois 04 Nov 2010 16:25 UTC 16 Nov 2021 10:04 UTC https://kar.kent.ac.uk/id/eprint/26019 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-7252-8515