Totally nonnegative cells and matrix Poisson varieties
نویسندگان
چکیده
منابع مشابه
Totally nonnegative cells and matrix Poisson varieties
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 compl...
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The space of m × p totally nonnegative real matrices has a stratification into totally nonnegative cells. The largest such cell is the space of totally positive matrices. There is a well-known criterion due to Gasca and Peña for testing a real matrix for total positivity. This criterion involves testing mp minors. In contrast, there is no known small set of minors for testing for total nonnegat...
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In this survey article, we describe recent work that connects three separate objects of interest: totally nonnegative matrices; quantum matrices; and matrix Poisson varieties. Mathematics Subject Classification 2000: 14M15, 15A48, 16S38, 16W35, 17B37, 17B63, 20G42, 53D17
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2011
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.07.010