Annals of Combinatorics

, Volume 9, Issue 1, pp 21–33

Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Original Paper
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Abstract.

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.

AMS Subject Classification.

05C12 82B41 51F15 

Keywords.

complex reflection groups reflection distances random walks 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden
  2. 2.Fachbereich Mathematik und InformatikPhilipps-Universität MarburgMarburgGermany

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