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

Gekhtman, Michael; Shapiro, Michael; Vainshtein, Alek

doi:10.1090/S0002-9939-02-06604-2

The number of connected components in double Bruhat cells for nonsimply-laced groups
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by Michael Gekhtman, Michael Shapiro and Alek Vainshtein PDF

Proc. Amer. Math. Soc. 131 (2003), 731-739 Request permission

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

Arkady Berenstein, Sergey Fomin, and Andrei Zelevinsky, Parametrizations of canonical bases and totally positive matrices, Adv. Math. 122 (1996), no. 1, 49–149. MR 1405449, DOI 10.1006/aima.1996.0057
Sergey Fomin and Andrei Zelevinsky, Double Bruhat cells and total positivity, J. Amer. Math. Soc. 12 (1999), no. 2, 335–380. MR 1652878, DOI 10.1090/S0894-0347-99-00295-7
Konstanze Rietsch, Intersections of Bruhat cells in real flag varieties, Internat. Math. Res. Notices 13 (1997), 623–640. With an appendix by G. Lusztig. MR 1459628, DOI 10.1155/S107379289700041X
Konstanze Rietsch, The intersection of opposed big cells in real flag varieties, Proc. Roy. Soc. London Ser. A 453 (1997), no. 1959, 785–791. MR 1447152, DOI 10.1098/rspa.1997.0043
B. Shapiro, M. Shapiro, and A. Vainshtein, Connected components in the intersection of two open opposite Schubert cells in $\textrm {SL}_n(\textbf {R})/B$, Internat. Math. Res. Notices 10 (1997), 469–493. MR 1446839, DOI 10.1155/S1073792897000329
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 1631773, DOI 10.1155/S1073792898000361
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.
Boris Shapiro, Michael Shapiro, Alek Vainshtein, and Andrei Zelevinsky, Simply laced Coxeter groups and groups generated by symplectic transvections, Michigan Math. J. 48 (2000), 531–551. Dedicated to William Fulton on the occasion of his 60th birthday. MR 1786504, DOI 10.1307/mmj/1030132732
Andrei Zelevinsky, Connected components of real double Bruhat cells, Internat. Math. Res. Notices 21 (2000), 1131–1154. MR 1800992, DOI 10.1155/S1073792800000568