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Double Bruhat Cells in Kac-Moody Groups and Integrable Systems
Double Bruhat Cells Kac-Moody Groups Integrable Systems Quantum Algebra
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2012/4/18
We construct a family of integrable Hamiltonian systems parametrized by pairs of Coxeter elements in the affine Weyl group. Their phase spaces are double Bruhat cells in the corresponding Kac-Moody gr...
Lower boundary hyperplanes of the canonical left cells in the affine Weyl group Wa（An-1）
affine Weyl groups left cells hyperplanes
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2011/9/28
Let F be any canonical left cell of the affine Weyl group Wa of type A. We describe the lower boundary hyperplanes for F, which answer two questions of Humphreys.
Left cells with a-value 4 in the affine weyl groups Ei(i=6,7,8)
two-sided cell left cell a-function distinguished involution left-connected
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2011/9/28
In the present paper,we give the respresentative set of left cell with a-value 4 in the affine weyl groups Ei(i=6,7,8),and the distinguished involution.Then we show that these left cells are left-conn...
Cells in Coxeter groups I
Cells Coxeter groups I
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2011/1/17
In their seminal paper [KL1] Kazhdan and Lusztig introduced the notion of cells.These are equivalence classes in a Coxeter group W and corresponding Hecke algebra H that can be defined combinatorially...