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On the factorization of the Haar measure on finite Coxeter groups

Urban R.

Probability and Mathematical Statistics

2011

Vol. 31, Fasc. 1

141--148

Let W be a finite Coxeter group and let λW be the Haar measure on W; i.e., λW(ω) = |W|−1 for every ω ∈ 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 {μ1..., μk} with their supports in T such that their convolution product μ1 ∗ ...∗ μk = λW:

Note on the factorization of the Haar measure on finite Coxeter groups

Urban R.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 1

173--180

In this note we show that for the finite Coxeter groups of types An, Bn, Dn, F4, G2 and I2 (m) it is possible to choose an appropriate set S of generators of order not greater than 2 and a finite set of probability measures {μ1,…, μk} with their supports in S such that μ1∗…∗ μk = λ, where λ (g) = |G|−1 for every g ∈ G.