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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The infinitesimal cone
of a totally positive semigroup


Author: Konstanze Rietsch
Journal: Proc. Amer. Math. Soc. 125 (1997), 2565-2570
MSC (1991): Primary 20G20, 15A48
MathSciNet review: 1401752
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Abstract: Given a complex reductive linear algebraic group split over $\mathbb {R}$ with a fixed pinning, it is shown that all elements of the Lie algebra $ \mathfrak {g}$ infinitesimal to the totally positive subsemigroup $G_{\ge 0}$ of $G$ lie in the totally positive cone $ \mathfrak {g}_{\ge 0}\subset \mathfrak {g} $.


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Additional Information

Konstanze Rietsch
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: rietsch@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03931-2
PII: S 0002-9939(97)03931-2
Keywords: Total positivity, linear algebraic groups
Received by editor(s): December 7, 1995
Received by editor(s) in revised form: April 16, 1996
Communicated by: Roe Goodman
Article copyright: © Copyright 1997 American Mathematical Society