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Total positivity in partial flag manifolds


Author: G. Lusztig
Journal: Represent. Theory 2 (1998), 70-78
MSC (1991): Primary 20G99
DOI: https://doi.org/10.1090/S1088-4165-98-00046-6
Published electronically: March 13, 1998
MathSciNet review: 1606402
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


References [Enhancements On Off] (What's this?)

  • [L1] George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston, Inc., Boston, MA, 1993. MR 1227098
  • [L2] 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
  • [L3] G. Lusztig, Total positivity and canonical bases, Algebraic groups and Lie groups (G. I. Lehrer, ed.), Cambridge Univ. Press, 1997, pp. 281-295.
  • [L4] 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
Email: gyuri@math.mit.edu

DOI: https://doi.org/10.1090/S1088-4165-98-00046-6
Received by editor(s): February 25, 1998
Published electronically: March 13, 1998
Additional Notes: Supported in part by the National Science Foundation
Article copyright: © Copyright 1998 American Mathematical Society