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.
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Received December 8, 2003
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Eriksen, N., Hultman, A. Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections. Ann. Comb. 9, 21–33 (2005). https://doi.org/10.1007/s00026-005-0238-y
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DOI: https://doi.org/10.1007/s00026-005-0238-y