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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Total positivity in partial flag manifolds
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by G. Lusztig PDF
Represent. Theory 2 (1998), 70-78 Request permission


The projective space of $\mathbf {R}^{n}$ has a natural open subset: the set of lines spanned by vectors with all coordinates $>0$. Such a subset can be defined more generally for any partial flag manifold of a split semisimple real algebraic group. The main result of the paper is that this subset can be defined by algebraic equalities and inequalities.
  • George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston, Inc., Boston, MA, 1993. MR 1227098
  • G. Lusztig, Total positivity in reductive groups, Lie theory and geometry, Progr. Math., vol. 123, Birkhäuser Boston, Boston, MA, 1994, pp. 531–568. MR 1327548, DOI 10.1007/978-1-4612-0261-5_{2}0
  • G. Lusztig, Total positivity and canonical bases, Algebraic groups and Lie groups (G. I. Lehrer, ed.), Cambridge Univ. Press, 1997, pp. 281-295.
  • G. Lusztig, Introduction to total positivity, Positivity in Lie theory: open problems, De Gruyter (to appear).
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Additional Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Email:
  • Received by editor(s): February 25, 1998
  • Published electronically: March 13, 1998
  • Additional Notes: Supported in part by the National Science Foundation
  • © Copyright 1998 American Mathematical Society
  • Journal: Represent. Theory 2 (1998), 70-78
  • MSC (1991): Primary 20G99
  • DOI:
  • MathSciNet review: 1606402