The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations

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.

AMS-TeX, 19 pages, no figures

References in corpus (1)

• Shifted Schur Functions

Cited by in corpus (15)

• Algebra of differential operators associated with Young diagrams
• On genus expansion of knot polynomials and hidden structure of Hurwitz tau-functions
• Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula
• Structure coefficients of the Hecke algebra of $(S_{2n},B_n)$
• Kerov's central limit theorem for Schur-Weyl measures of parameter 1/2
• Connection between cut-and-join and Casimir operators
• Spin Hurwitz theory and Miwa transform for the Schur Q-functions
• The Chiral Ring of a Symmetric Orbifold and its Large N Limit
• Asymptotics of the Gelfand models of the symmetric groups
• The top-degree part in the Matchings-Jack Conjecture
• On algebras of double cosets of symmetric groups with respect to Young subgroups
• Shifted genus expanded ${\mathcal{W}}_{\infty }$ algebra and shifted Hurwtiz numbers
• Symmetric group characters of almost square shape
• Bijection between trees in Stanley character formula and factorizations of a cycle
• The algebra of conjugacy classes of the wreath product of a finite group with the symmetric group