Symmetric Representation Rings are $\lambda$-Rings
The representation ring of an affine algebraic group scheme can be endowed with the structure of a (special) $\lambda$-ring. We show that the same is true for the ring of symmetric representations, i.e. for the Grothendieck-Witt ring of the representation category, for any affine algebraic group scheme over a field of characteristic not two.
Comment: 36 pages. Some changes of notation
Representation theory for linear algebraic groups, Frobenius induction, Burnside and representation rings, \(\lambda\)-ring, Witt groups of rings, Group schemes, Mathematics - K-Theory and Homology, Arithmetic rings and other special commutative rings, Grothendieck-Witt ring, 20G05, 18F25, algebraic group scheme, Mathematics - Representation Theory
Representation theory for linear algebraic groups, Frobenius induction, Burnside and representation rings, \(\lambda\)-ring, Witt groups of rings, Group schemes, Mathematics - K-Theory and Homology, Arithmetic rings and other special commutative rings, Grothendieck-Witt ring, 20G05, 18F25, algebraic group scheme, Mathematics - Representation Theory
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