Totally nonnegative cells and matrix Poisson varieties

@inproceedings{Goodearl2010TotallyNC,
  title={Totally nonnegative cells and matrix Poisson varieties},
  author={Kenneth R Goodearl and St{\'e}phane Launois and T. Lenagan},
  year={2010}
}
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… CONTINUE READING