A Hopf-algebra approach to inner plethysm

DOI10.1006/aima.1994.1019zbMath0830.20027OpenAlexW2048519828MaRDI QIDQ1328493

Jean-Yves Thibon, Thomas Scharf

Publication date: 24 January 1996

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/67278b0b7199561a86798294a086c3b5f6e0d99a

zbMATH Keywords

symmetric groupsHopf algebrasalgebra of symmetric functionscomplex representation ringsgroup charactersAdams operatorsinner plethysm

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Frobenius induction, Burnside and representation rings (19A22) Hopf algebras (aspects of homology and homotopy of topological groups) (57T05)

Related Items (20)

Symmetric group characters as symmetric functions ⋮ Unnamed Item ⋮ THE DIRICHLET HOPF ALGEBRA OF ARITHMETICS ⋮ Products of symmetric group characters ⋮ The \((1-\mathbb{E})\)-transform in combinatorial Hopf algebras ⋮ Character polynomials and the restriction problem ⋮ Analogies between finite-dimensional irreducible representations of SO(2n) and infinite-dimensional irreducible representations of Sp(2n,R). II. Plethysms ⋮ Algebraic random walks in the setting of symmetric functions ⋮ Abacus-histories and the combinatorics of creation operators ⋮ A symmetry of the descent algebra of a finite Coxeter group. ⋮ On the decomposition of tensor representations of symmetric groups ⋮ Witt vectors. Part 1 ⋮ A symmetry property of Solomon's algebra and of higher Lie characters ⋮ Branching from the general linear group to the symmetric group and the principal embedding ⋮ A comment on the combinatorics of the vertex operator \(\Gamma_{(t|X)}\) ⋮ The Hopf structure of symmetric group characters as symmetric functions ⋮ Commutative combinatorial Hopf algebras. ⋮ Polynomial induction and the restriction problem ⋮ A combinatorial model for the decomposition of multivariate polynomial rings as \(S_n\)-modules ⋮ Howe duality of the symmetric group and a multiset partition algebra

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