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Contents of PMS, Vol. 31, Fasc. 1,
pages -
 

ON THE FACTORIZATION OF THE HAAR MEASURE ON FINITE COXETER GROUPS

Roman Urban

Abstract: Let W be a finite Coxeter group and let λ
  W  be the Haar measure on W, i.e., λ  (w) = |W |-1
 W  for every w ∈ W. We prove that there exist a symmetric set T ⁄= W of generators of W consisting of elements of order not greater than 2 and a finite set of probability measures (μ ,...,μ )
  1     k with their supports in T such that their convolution product μ *...*μ  = λ  .
 1       k   W

2000 AMS Mathematics Subject Classification: Primary: 60B15; Secondary: 20F55.

Keywords and phrases: Finite Coxeter groups, parabolic subgroups, convolution of probability measures, factorization of measure, uniform distribution, Haar measure, subgroup algorithm.

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