75.6 Operations and functions for Coxeter groups
All permutation group operations are defined on Coxeter groups. However,
the following operations and functions have been rewritten or added,
respectively, to take advantage of the particular structure of real
Two Coxeter data are equal if they are equal as permutation groups
and the fields
(independently of the value of any other bound fields). Also the
fields .omega should be equal (if the field is absent ---
not specified --- this is considered specifying the trivial group).
prints a Coxeter group in a form that can be input back in
GAP as a Coxeter group.
uses the classification of Coxeter groups to work faster
(specifically, uses the function
returns the set of elements. They are computed using
CoxeterElementsLength. (Note that in an earlier version of the
package the elements were sorted by length. You can still get such a
Concatenation( List( [1..W.N], i -
CartanType of the Cartan matrix.
prints the Dynkin diagram corresponding to the
CartanName of the
Uses classification of Coxeter groups to work
faster, and the resulting list is given in the same order as the
ChevieClassInfo (see ChevieClassInfo).
Uses the classification of Coxeter groups to work faster,
and the result has better labeling than the default (see Chapter
Character tables for Coxeter groups).
Is part of the Coxeter groups operations record in
order to have versions for Coxeter groups and Coxeter cosets. This
function returns additional information on the classes which is
contained in the character table, but this function returns it
without first computing
CharTable(W). See the explicit
description in ChevieClassInfo.
Is part of the Coxeter groups operations record in order
to have versions for Coxeter groups and Coxeter cosets. This
function returns the list of parameters for the irreducible
characters of W: partitions for type
A, double partitions for
B, etc... This is used by functions which return information
for individual characters, like
Is part of the Coxeter groups operations record in order to
have versions for Coxeter groups and Coxeter cosets. This function
takes as argument a parameter for a character (see
returns a string which is used to label the character is various
This function returns additional information on the
irreducible characters, see ChevieCharInfo for more details.
classification of Coxeter groups to work faster.
PositionClass(W,x) returns the index of the conjugacy class of x
in the list of the classes of W, see PositionClass.
These functions require the package "chevie" (see RequirePackage).
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