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

• Autorzy: Urban R.
• Języki publikacji: EN

Abstrakty

EN

In this note we show that for the finite Coxeter groups of types A_n, B_n, D_n, 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,…, μ_k} with their supports in S such that μ₁∗…∗ μ_k = λ, where λ (g) = |G|⁻¹ for every g ∈ G.

Słowa kluczowe

EN

finite Coxeter groups; factorization; Haar measure; Fourier transform

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2004
• Tom: Vol. 24, Fasc. 1
• Strony: 173--180
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Urban R.

• Institute of Mathematics, University of Wrocław. pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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• [3] P. Diaconis, Application of non-cummutative Fourier analysis to probability problems, Lecture Notes in Math. No 1362, Springer, 1982, pp. 51-100.
• [4] M. Geck and G. Pfeiffer, Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras, London Math. Soc. Monographs, 2000.
• [5] U. Grenander, Probability on Algebraic Structures, Wiley, New York 1963.
• [6] L. C. Grove and C. T. Benson, Finite Reflection Groups, Graduate Texts in Math. 99, Springer, 1985.
• [7] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 2, Springer, Berlin 1970.
• [8] J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, Cambridge-New York 1990.
• [9] J. P. Serre, Linear Representation of Finite Groups, Springer, New York 1977.
• [10] M. Ullrich and K. Urbanik, A limit theorem for random variables in compact topological groups, Colloq. Math. 7 (1960), pp. 191-198.
• [11] R. Urban, Some remarks on the random walk on finite groups, Colloq. Math. 74 (1997), pp. 287-298.