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Total Positivity in Reductive Groups

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Lie Theory and Geometry

Part of the book series: Progress in Mathematics ((PM,volume 123))

Abstract

An invertible n×n matrix with real entries is said to be totally ≥0 (resp. totally >0) if all its minors are ≥0 (resp. >0). This definition appears in Schoenberg’s 1930 paper [S] and in the 1935 note [GK] of Gantmacher and Krein. (For a recent survey of totally positive matrices, see [A].)

Supported in part by the National Science Foundation.

Dedicated to Bert Kostant on his 65th birthday

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Author information

Authors and Affiliations

  1. Department of Mathematics, M.I.T., 02139, Cambridge, MA, USA

    G. Lusztig

  2. Institut Mittag-Leffler, Auravägen 17, S-18262, Djursholm, Sweden

    G. Lusztig

Authors
  1. G. Lusztig
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Penn State University, 16802, University Park, PA, USA

    Jean-Luc Brylinski  & Ranee Brylinski  & 

  2. Department of Mathematics, MIT, 02139, Cambridge, MA, USA

    Victor Guillemin  & Victor Kac  & 

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© 1994 Springer Science+Business Media New York

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Lusztig, G. (1994). Total Positivity in Reductive Groups. In: Brylinski, JL., Brylinski, R., Guillemin, V., Kac, V. (eds) Lie Theory and Geometry. Progress in Mathematics, vol 123. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0261-5_20

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  • DOI: https://doi.org/10.1007/978-1-4612-0261-5_20

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6685-3

  • Online ISBN: 978-1-4612-0261-5

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