82.11 HeckeCharValuesGood

HeckeCharValuesGood( HW, w )

Let HW be a Hecke algebra for the Coxeter group CoxeterGroup(HW), let w be a good element of CoxeterGroup(HW) in the sense of GM97, and let d be the order of w.

HeckeCharValuesGood computes the values of the irreducible characters of the Iwahori-Hecke algebra HW on T_w^d. The point is that the character table of the Hecke algebra is not used, and that all the eigenvalues of T_w^d are monomials in HW.parameters, so this can be used to find the absolute value of the eigenvalues of T_w, a step towards computing the character table of the Hecke algebra.

We continue the example in HeckeCentralMonomial:

    gap> HeckeCharValuesGood( H, [ 1, 2, 3 ] );
    [ v^0, v^60, 5*v^24, 5*v^36, 3*v^20, 3*v^20, 3*v^40, 3*v^40, 4*v^30, 
      4*v^30 ]

This function requires the package "chevie" (see RequirePackage). Previous Up Top
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GAP 3.4.4
April 1997