2 SERGEY FOMIN AND ANDREI ZELEVINSKYin

2 Sergey Fomin and Andrei Zelevinsky

1. Introduction This paper focuses on the properties of Schubert cells as quasi-projective subva-rieties of a generalized ag variety. More speciically, we investigate the problem of distinguishing between diierent Schubert cells using vanishing patterns of generalized Pl ucker coordinates.

Sergey Fomin And

Total Positivity: Tests and Parametrizations

Sergey Fomin and Andrei Zelevinsky

In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.

Introduction to Cluster Algebras Chapters 1–3

Preface This is a preliminary draft of Chapters 1–3 of our forthcoming textbook Introduction to cluster algebras, joint with Andrei Zelevinsky (1953–2013). We expect to post additional chapters in the not so distant future. This book grew from the ten lectures given by Andrei at the NSF CBMS conference on Cluster Algebras and Applications at North Carolina State University in June 2006. The mat...