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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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
MathSciNet review: 1937410
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Abstract | References | Similar articles | Additional information

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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A. Berenstein, S. Fomin, and A. Zelevinsky, Parametrizations of canonical bases and totally positive matrices, Adv. Math. 122 (1996), 49-149. MR 98j:17008

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S. Fomin and A. Zelevinsky, Double Bruhat cells and total positivity, J. Amer. Math. Soc. 12 (1999), 335-380. MR 2001f:20097

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K. Rietsch, Intersections of Bruhat cells in real flag varieties, Internat. Math. Res. Notices (13) (1997), 623-640. MR 98f:14038

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K. Rietsch, The intersection of opposed big cells in real flag varieties, Proc. Roy. Soc. London Ser. A 453 (1997), 785-791. MR 98d:14064

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B. Shapiro, M. Shapiro, and A. Vainshtein, Connected components in the intersection of two open opposite Schubert cells in ${\text{S}L}_{n}({\mathbb R})/B$, Internat. Math. Res. Notices (10) (1997), 469-493. MR 98e:14054

[SSV98]
B. Shapiro, M. Shapiro, and A. Vainshtein, Skew-symmetric vanishing lattices and intersections of Schubert cells, Internat. Math. Res. Notices (11) (1998), 563-588. MR 2000e:14093

[SSV99]
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.

[SSVZ]
B. Shapiro, M. Shapiro, A. Vainshtein, and A. Zelevinsky, Simply-laced Coxeter groups and groups generated by symplectic transvections, Michigan Mathematical Journal 48 (2000), 531-552. MR 2001g:20050

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A. Zelevinsky, Connected components of real double Bruhat cells, Internat. Math. Res. Notices (21) (2000), 1131-1154. MR 2001k:14094

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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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