منابع مشابه
Regular Cell Complexes in Total Positivity
Fomin and Shapiro conjectured that the link of the identity in the Bruhat stratification of the totally nonnegative real part of the unipotent radical of a Borel subgroup in a semisimple, simply connected algebraic group defined and split over R is a regular CW complex homeomorphic to a ball. The main result of this paper is a proof of this conjecture. This completes the solution of the questio...
متن کاملRegular Cell Complexes in Total Positivity
This paper proves a conjecture of Fomin and Shapiro that their combinatorial model for any Bruhat interval for any finite Weyl group is a regular CW complex which is homeomorphic to a ball. The model consists of a stratified space which may be regarded as the link of an open cell in a larger closed cell, all within the totally nonnegative part of the unipotent radical of an algebraic group. A k...
متن کاملSorting Orders, Subword Complexes, Bruhat Order and Total Positivity
In this note we construct a poset map from a Boolean algebra to the Bruhat order which unveils an interesting connection between subword complexes, sorting orders, and certain totally nonnegative spaces. This relationship gives a simple new proof that the proper part of Bruhat order is homotopy equivalent to the proper part of a Boolean algebra — that is, to a sphere. We also obtain a geometric...
متن کاملTotal positivity in Schubert varieties
We extend the results of [2] on totally positive matrices to totally positive elements in arbitrary semisimple groups. Mathematics Subject Classification (1991). 14M15, 22E46, 15A48.
متن کاملRegulators and Total Positivity
The classical regulator R of a number field K is given [F1] by a rapidly convergent series of the form R w = ∞
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2013
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-013-0480-1