On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cells

1985 ◽  
Vol 79 (3) ◽  
pp. 499-511 ◽  
Author(s):  
Vinay V. Deodhar
Keyword(s):  
Bruhat Cells

scholarly journals DOUBLE BRUHAT CELLS AND SYMPLECTIC GROUPOIDS

2017 ◽  
Vol 23 (3) ◽  
pp. 765-800 ◽  
Author(s):  
JIANG-HUA LU ◽  
VICTOR MOUQUIN
Keyword(s):  
Bruhat Cells ◽  
Symplectic Groupoids

A UNIPOTENT GROUP ACTION ON A FLAG MANIFOLD AND "GAP SEQUENCES" OF PERMUTATIONS

2003 ◽  
Vol 02 (02) ◽  
pp. 215-222 ◽  
Author(s):  
BARBARA A. SHIPMAN
Keyword(s):  
Hamiltonian System ◽  
Toda Lattice ◽  
Initial Conditions ◽  
Flag Manifold ◽  
Unipotent Group ◽  
Unipotent Subgroup ◽  
Bruhat Cells ◽  
Generic Orbit ◽  
Gap Sequence ◽  
Gap Sequences

There is a unipotent subgroup of Sl(n, C) whose action on the flag manifold of Sl(n, C) completes the flows of the complex Kostant–Toda lattice (a Hamiltonian system in Lax form) through initial conditions where all the eigenvalues coincide. The action preserves the Bruhat cells, which are in one-to-one correspondence with the elements of the permutation group Σn. A generic orbit in a given cell is homeomorphic to Cm, where m is determined by the "gap sequence" of the permutation, which lists the number inversions of each degree.

scholarly journals Cluster algebras III: Upper bounds and double Bruhat cells

2005 ◽  
Vol 126 (1) ◽  
pp. 1-52 ◽  
Author(s):  
Arkady Berenstein ◽  
Sergey Fomin ◽  
Andrei Zelevinsky
Keyword(s):  
Upper Bounds ◽  
Cluster Algebras ◽  
Bruhat Cells

scholarly journals Explicit Forms of Cluster Variables on Double Bruhat Cells $G^{u,e}$ of Type C

2017 ◽  
Vol 39 (3) ◽  
pp. 643-678
Author(s):  
Yuki KANAKUBO ◽  
Toshiki NAKASHIMA
Keyword(s):  
Bruhat Cells ◽  
Type C

scholarly journals The Full Symmetric Toda Flow and Intersections of Bruhat Cells

2020 ◽  
Author(s):  
Yuri B. Chernyakov ◽  
◽  
Georgy I. Sharygin ◽  
Alexander S. Sorin ◽  
Dmitry V. Talalaev ◽  
...  
Keyword(s):  
Bruhat Cells ◽  
Toda Flow
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