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

o3 : List
i4 : underBruhat(L1)

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

o4 : List