A Hopf-algebra approach to inner plethysm. (English) Zbl 0830.20027

Scharf, Thomas; Thibon, Jean-Yves

Adv. Math. 104, No. 1, 30-58 (1994).

Summary: We use the Hopf algebra structure of the algebra of symmetric functions to study the Adams operators of the complex representation rings of symmetric groups, and give new proofs of Littlewood’s formulas for inner plethysm. We also study the Adams operations for orthogonal and symplectic group characters.

MSC:

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

Keywords:

Hopf algebras; algebra of symmetric functions; Adams operators; complex representation rings; symmetric groups; inner plethysm; group characters