Double Bruhat cells and total positivity
Sergey Fomin, Andrei Zelevinsky
TL;DR
This paper investigates the structure of intersections of opposite Bruhat cells within semisimple complex Lie groups and explores their connections to totally nonnegative varieties, advancing understanding of total positivity in algebraic groups.
Contribution
It introduces new insights into the geometry of Bruhat cell intersections and their relation to total positivity, providing a framework for further algebraic and geometric analysis.
Findings
Characterization of intersections of opposite Bruhat cells
Development of total positivity varieties related to these intersections
New geometric descriptions of totally nonnegative parts
Abstract
We study intersections of opposite Bruhat cells in a semisimple complex Lie group, and associated totally nonnegative varieties.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Combinatorial Mathematics · Algebraic Geometry and Number Theory