Double Bruhat cells and total positivity

Fomin, Sergey¹ ; Zelevinsky, Andrei²

¹ Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
² Department of Mathematics, Northeastern University, Boston, Massachusetts 02115

Journal of the American Mathematical Society, Tome 12 (1999) no. 2, pp. 335-380

Résumé

We study the totally nonnegative variety $G_{\ge 0}$ in a semisimple algebraic group $G$. These varieties were introduced by G. Lusztig, and include as a special case the variety of unimodular matrices of a given order whose all minors are nonnegative. The geometric framework for our study is provided by intersecting $G_{\ge 0}$ with double Bruhat cells (intersections of cells of the two Bruhat decompositions of $G$ with respect to opposite Borel subgroups).

Détail

DOI : 10.1090/S0894-0347-99-00295-7

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