Character Theory of Symmetric Groups, Subgroup Growth of Fuchsian Groups, and Random Walks

2003/05/18 by Thomas W. Mueller, Mueller, Thomas W., Jan‐Christoph Schlage‐Puchta +2 · 1 citation
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Graph theory and applications #math.GR #math.RT #msc:20C30 #msc:20E07 #msc:60G50

paper · pdf · doi:10.48550/arxiv.math/0305260

57 pages, submitted to Acta Mathematica

arxiv created 2003/05/18 · arxiv updated 2009/11/30

Abstract

We derive an asymptotic expansion for the subgroup of arbitrary Fuchsian groups and some other classes of large groups. Moreover, the main conjecture for Random Walks on symmetric groups is established in full generality. Both problems require subtle estimates of character values and root number multiplicities for symmetric groups, which are also of independent interest.

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• Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions

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