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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 number of connected components in double Bruhat cells for nonsimply-laced groups


Authors: Michael Gekhtman, Michael Shapiro and Alek Vainshtein
Journal: Proc. Amer. Math. Soc. 131 (2003), 731-739
MSC (2000): Primary 20F55; Secondary 05E15, 14M15
Published electronically: June 12, 2002
MathSciNet review: 1937410
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Abstract: We compute the number of connected components in a generic real double Bruhat cell for series $B_{n}$ and $C_{n}$ and an exceptional group $F_{4}$.


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Additional Information

Michael Gekhtman
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: Michael.Gekhtman.1@nd.edu

Michael Shapiro
Affiliation: Matematiska Institutionen, KTH, Stockholm, Sweden
Address at time of publication: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
Email: mshapiro@math.kth.se, mshapiro@math.msu.edu

Alek Vainshtein
Affiliation: Departments of Mathematics and of Computer Science, University of Haifa, Israel 31905
Email: alek@mathcs.haifa.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06604-2
PII: S 0002-9939(02)06604-2
Keywords: Double Bruhat cells, Coxeter graphs, groups generated by transvections
Received by editor(s): May 8, 2001
Received by editor(s) in revised form: October 25, 2001
Published electronically: June 12, 2002
Communicated by: John R. Stembridge
Article copyright: © Copyright 2002 American Mathematical Society