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WeylGroups :: intervalBruhat(WeylGroupElement,WeylGroupElement)

intervalBruhat(WeylGroupElement,WeylGroupElement) -- elements between two given ones for the Bruhat order on a Weyl group

Synopsis

Description

i1 : R=rootSystemA(3)

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

o1 : RootSystem
i2 : w1 = reduce(R,{2,1,2})

o2 = WeylGroupElement{RootSystem{...8...}, | -1 |}
                                           | -1 |
                                           |  3 |

o2 : WeylGroupElement
i3 : w2 = reduce(R,{1,2,1,3,2})

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

o3 : WeylGroupElement
i4 : myInterval=intervalBruhat(w1,w2)

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

o4 : HasseDiagram

Each row of the Hasse diagram contains the elements of a certain length together with their links to the next row.

i5 : myInterval#1

o5 = {{WeylGroupElement{RootSystem{...8...}, | -2 |}, {{0, |  0 |}}},
                                             | -1 |        | -1 |    
                                             |  2 |        |  2 |    
     ------------------------------------------------------------------------
     {WeylGroupElement{RootSystem{...8...}, |  1 |}, {{0, | -1 |}}}}
                                            | -3 |        |  1 |
                                            |  1 |        |  1 |

o5 : List