A Hopf-Algebra Approach to Inner Plethysm

T Scharf (1) , Jean-Yves Thibon

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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 we give new proofs of all of Littlewood's formulas for inner plethysm. We also study the Adams operations for orthogonal and symplectic group characters. (C) 1994 Academic Press, Inc.

Domaines: Physique mathématique [math-ph]

T Scharf, Jean-Yves Thibon. A Hopf-Algebra Approach to Inner Plethysm. Advances in Mathematics, 1994, 104 (1), pp.30--58. ⟨10.1006/aima.1994.1019⟩. ⟨hal-00693558⟩