Goodearl, Ken and Launois, S. and Lenagan, T.H.
(2011)
*Totally nonnegative cells and Matrix Poisson varieties.*
Advances in Mathematics, 226
(1).
pp. 779-826.
ISSN 0001-8708.
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Official URL http://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 |
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Subjects: | Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Q Science > QA Mathematics (inc Computing science) > QA564 Algebraic Geometry |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics |

Depositing User: | Stephane Launois |

Date Deposited: | 04 Nov 2010 16:25 |

Last Modified: | 15 Nov 2011 10:17 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/26019 (The current URI for this page, for reference purposes) |

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