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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Double Bruhat cells and total positivity
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by Sergey Fomin and Andrei Zelevinsky PDF
J. Amer. Math. Soc. 12 (1999), 335-380

Abstract:

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).
References
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Additional Information
  • Sergey Fomin
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 230455
  • ORCID: 0000-0002-4714-6141
  • Email: fomin@math.mit.edu
  • Andrei Zelevinsky
  • Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
  • Email: andrei@neu.edu
  • Received by editor(s): February 12, 1998
  • Additional Notes: The authors were supported in part by NSF grants #DMS-9400914, #DMS-9625511, and #DMS-9700927, and by MSRI (NSF grant #DMS-9022140).
  • © Copyright 1999 by Sergey Fomin and Andrei Zelevinsky
  • Journal: J. Amer. Math. Soc. 12 (1999), 335-380
  • MSC (1991): Primary 22E46; Secondary 05E15, 15A23
  • DOI: https://doi.org/10.1090/S0894-0347-99-00295-7
  • MathSciNet review: 1652878