Regular Cell Complexes in Total Positivity
نویسنده
چکیده
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 key ingredient is a new, readily verifiable criterion for determining which finite CW complexes are regular involving an interplay of topology with combinatorics.
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...
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