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
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2017 ◽  
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JIANG-HUA LU ◽  
VICTOR MOUQUIN

2003 ◽  
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BARBARA A. SHIPMAN

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.


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Sergey Fomin ◽  
Andrei Zelevinsky

2017 ◽  
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Toshiki NAKASHIMA
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Georgy I. Sharygin ◽  
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