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Expected Reflection Distance in G(r, 1, n) After a Fixed Number of Reflections
Niklas Eriksen1, and Axel Hultman2
1Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
niklase@math.kth.se
2Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, 35032 Marburg Germany
axel@mathematik.uni-marburg.de
Annals of Combinatorics 9 (1) p.21-33 March, 2005
AMS Subject Classification: 05C12, 82B41, 51F15
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.
Keywords: complex reflection groups, reflection distances, random walks

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