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

Author(s): Michael Gekhtman; Michael Shapiro; Alek Vainshtein
Journal: Proc. Amer. Math. Soc. 131 (2003), 731-739.
MSC (2000): Primary 20F55; Secondary 05E15, 14M15
Posted: June 12, 2002
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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 $F_{4}$.

References:

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B. Shapiro, M. Shapiro, and A. Vainshtein, Intersections of Schubert cells and groups generated by symplectic transvections, Proc. 11th Conf. Formal Power Series and Algebraic Combinatorics (FPSAC'99), 1999, pp. 530-533.

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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: 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
Posted: June 12, 2002
Communicated by: John R. Stembridge
Copyright of article: Copyright 2002, American Mathematical Society

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