Total positivity in partial flag manifolds

Name: Total positivity in partial flag manifolds
Creator: Lusztig, G.
Keywords: Grassmannian, projective space, Linear algebraic groups over the reals, the complexes, the quaternions, 0101 mathematics, Grassmannians, Schubert varieties, flag manifolds, 01 natural sciences

Lusztig, G.

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Representation Theory of the American Mathematical Society

Article . 1998 . Peer-reviewed

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https://dx.doi.org/10.1090/s10...

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Total positivity in partial flag manifolds

descriptionPublicationkeyboard_double_arrow_right Article 13 Mar 1998 English Publisher:American Mathematical Society (AMS)Journal:Representation Theory of the American Mathematical Society, volume 2, pages 70-78 (eissn: 1088-4165,

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Authors: Lusztig, G.;

doi: 10.1090/s1088-4165-98-00046-6

Total positivity in partial flag manifolds

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Abstract

The projective space of R n \mathbf {R}^{n} has a natural open subset: the set of lines spanned by vectors with all coordinates > 0 >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.

Related Organizations

Massachusetts Institute of Technology
United States

Keywords

Grassmannian, projective space, Linear algebraic groups over the reals, the complexes, the quaternions, Grassmannians, Schubert varieties, flag manifolds

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