The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations

2003/02/18 by Vladimir Ivanov, Sergei Kerov · 3 citations
Mathematics · #math.CO #math.RT #msc:05E10 #msc:20B30 #msc:20C30 #msc:20C32 #msc:20E45

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published as Journal of Mathematical Sciences (Kluwer) 107 (2001) no.5 4212-4230 · AMS-TeX, 19 pages, no figures

arxiv created 2003/02/18 · arxiv updated 2009/11/30

Abstract

We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We describe its structure, representations, and characters. We also discuss filtrations on the subalgebra of invariants in the semigroup algebra.

Cited by

• Inverse Monoid Topological Quantum Field Theories and Open-Closed Grand Canonical Symmetric Orbifolds
• Grand-Canonical Symmetric Orbifold Theories
• On algebras of conjugacy classes of symmetric groups with respect to Young subgroups

Related

• Conjugacy in Permutation Representations of the Symmetric Group
• Symmetric groups and conjugacy classes
• On algebras of conjugacy classes of symmetric groups with respect to Young subgroups
• Sign conjugacy classes in symmetric groups
• Combinatorial And Algebraic Properties Of Nilpotent And Idempotent Conjugacy Classes: A Study In Partial One-To-One Transformation Semigroups