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

DOI: 10.1007/s00026-005-0238-y

Cite this article as:
Eriksen, N. & Hultman, A. Ann. Comb. (2005) 9: 21. doi:10.1007/s00026-005-0238-y
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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.

05C1282B4151F15

Keywords.

complex reflection groupsreflection distancesrandom walks

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