The geometry of products of minors

We consider the Newton polytope Σ(m,n) of the product of all minors of an m× n matrix of indeterminates. Using the fact that this polytope is the secondary polytope of the product Δ _m-1 ×Δ _n-1 of simplices, and thus has faces corresponding to coherent polyhedral subdivisions of Δ _m-1 ×Δ _n-1 , we study facets of Σ(m,n) , which correspond to the coarsest, nontrivial such subdivisions. We make use of the relation between secondary and fiber polytopes, which in this case gives a representation of Σ(m,n) as the Minkowski average of all m × n transportation polytopes. <lsiheader> <onlinepub>7 August, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>20n2p231.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>no <sectionname> </lsiheader> Received August 7, 1996, and in revised form April 4, 1997.