, Volume 9, Issue 1, pp 21-33

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

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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.

Received December 8, 2003