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WeylGroups :: underBruhat(BasicList)

underBruhat(BasicList) -- Weyl group elements just under the ones in the list for the Bruhat order

Synopsis

Description

i1 : R=rootSystemA(3)

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

o1 : RootSystem
i2 : L=underBruhat(longestWeylGroupElement(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 : L1=apply(L,x->x#0)

o3 = {WeylGroupElement{RootSystem{...8...}, | -1 |},
                                            | -2 |  
                                            | 1  |  
     ------------------------------------------------------------------------
     WeylGroupElement{RootSystem{...8...}, | -2 |},
                                           | 1  |  
                                           | -2 |  
     ------------------------------------------------------------------------
     WeylGroupElement{RootSystem{...8...}, | 1  |}}
                                           | -2 |
                                           | -1 |

o3 : List
i4 : underBruhat(L1)

o4 = {{WeylGroupElement{RootSystem{...8...}, | 1  |}, {{0, | 0  |}, {2, | 2 
                                             | -3 |        | -1 |       | -1
                                             | 1  |        | 2  |       | 0 
     ------------------------------------------------------------------------
     |}}}, {WeylGroupElement{RootSystem{...8...}, | 2  |}, {{1, | -1 |}, {2,
     |                                            | -1 |        | 1  |      
     |                                            | -2 |        | 1  |      
     ------------------------------------------------------------------------
     | -1 |}}}, {WeylGroupElement{RootSystem{...8...}, | -3 |}, {{0, | 1  |},
     | 2  |                                            | 2  |        | 1  |  
     | -1 |                                            | -1 |        | -1 |  
     ------------------------------------------------------------------------
     {1, | 2  |}}}, {WeylGroupElement{RootSystem{...8...}, | -2 |}, {{0, | -1
         | -1 |                                            | -1 |        | 2 
         | 0  |                                            | 2  |        | -1
     ------------------------------------------------------------------------
     |}, {1, | 1  |}}}, {WeylGroupElement{RootSystem{...8...}, | -1 |}, {{1,
     |       | 1  |                                            | 2  |       
     |       | -1 |                                            | -3 |       
     ------------------------------------------------------------------------
     | 0  |}, {2, | -1 |}}}}
     | -1 |       | 1  |
     | 2  |       | 1  |

o4 : List