Mathematics – Algebraic Geometry
Scientific paper
2009-05-22
Mathematics
Algebraic Geometry
46 pages
Scientific paper
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.
Goodearl K. R.
Launois Stephane
Lenagan T. H.
No associations
LandOfFree
Totally nonnegative cells and matrix Poisson varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Totally nonnegative cells and matrix Poisson varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Totally nonnegative cells and matrix Poisson varieties will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-325294