Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165



Total positivity in partial flag manifolds

Author: G. Lusztig
Journal: Represent. Theory 2 (1998), 70-78
MSC (1991): Primary 20G99
Published electronically: March 13, 1998
MathSciNet review: 1606402
Full-text PDF Free Access

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?)

  • 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
  • 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).

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (1991): 20G99

Retrieve articles in all journals with MSC (1991): 20G99

Additional Information

G. Lusztig
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID: 117100

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