Total positivity in partial flag manifolds
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- by G. Lusztig
- Represent. Theory 2 (1998), 70-78
- DOI: https://doi.org/10.1090/S1088-4165-98-00046-6
- Published electronically: March 13, 1998
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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
- 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).
Bibliographic Information
- G. Lusztig
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Email: gyuri@math.mit.edu
- 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: https://doi.org/10.1090/S1088-4165-98-00046-6
- MathSciNet review: 1606402