The Representation Ring of a Simply Connected Lie Group as a λ-Ring

Abstract

Adams and Conway have stated without proof a result which says, roughly speaking, that the representation ring R(G) of a compact, connected Lie group G is generated as a λ-ring by elements in 1-to-1 correspondence with the branches of the Dynkin diagram. In this note we present an elementary proof of this.

Keywords:

• Dynkin diagrams
• λ-rings
• Lie groups

Mathematics Subject Classification:

• 22E46

ACKNOWLEDGMENT

I would like to thank Skip Garibaldi for his suggestions.

Notes

¹Such weights do exist, cf. the 26-dimensional representation of F ₄ which has two zero weights.

Communicated by E. I. Zelmanov.