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 has a natural open subset: the set of lines spanned by vectors with all coordinates . 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.

**[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