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WeylGroups :: aboveBruhat(WeylGroupElement)

aboveBruhat(WeylGroupElement) -- Weyl group elements just above a given one for the Bruhat order

Synopsis

Description

i1 : R=rootSystemA(3)

o1 = RootSystem{...8...}

o1 : RootSystem
i2 : L=aboveBruhat(neutralWeylGroupElement(R))

o2 = {{WeylGroupElement{RootSystem{...8...}, | -1 |}, | 2  |},
                                             | 2  |   | -1 |  
                                             | 1  |   | 0  |  
     ------------------------------------------------------------------------
     {WeylGroupElement{RootSystem{...8...}, | 2  |}, | -1 |},
                                            | -1 |   | 2  |  
                                            | 2  |   | -1 |  
     ------------------------------------------------------------------------
     {WeylGroupElement{RootSystem{...8...}, | 1  |}, | 0  |}}
                                            | 2  |   | -1 |
                                            | -1 |   | 2  |

o2 : List
i3 : apply(L,x->reducedDecomposition (x#0))

o3 = {{1}, {2}, {3}}

o3 : List