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Totally nonnegative and oscillatory elements in semisimple groups

Authors: Sergey Fomin and Andrei Zelevinsky
Journal: Proc. Amer. Math. Soc. 128 (2000), 3749-3759
MSC (2000): Primary 22E46; Secondary 14M15, 15A48, 20F55
Published electronically: June 7, 2000
MathSciNet review: 1694341
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Abstract | References | Similar Articles | Additional Information

Abstract: We generalize the well known characterizations of totally nonnegative and oscillatory matrices, due to F. R. Gantmacher, M. G. Krein, A. Whitney, C. Loewner, M. Gasca, and J. M. Peña to the case of an arbitrary complex semisimple Lie group.

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Additional Information

Sergey Fomin
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Andrei Zelevinsky
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115

Keywords: Total positivity, oscillatory element, semisimple Lie group
Received by editor(s): November 18, 1998
Received by editor(s) in revised form: February 26, 1999
Published electronically: June 7, 2000
Additional Notes: The authors were supported in part by NSF grants #DMS-9625511 and #DMS-9700927
Communicated by: John R. Stembridge
Article copyright: © Copyright 2000 Sergey Fomin and Andrei Zelevinsky