  We describe a Hopf algebraic approach to the Grothendieck ring of
representations of subgroups $H_\pi$ of the general linear group GL(n) which
stabilize a tensor of Young symmetry $\{\pi\}$. It turns out that the
representation ring of the subgroup can be described as a Hopf algebra twist,
with a 2-cocycle derived from the Cauchy kernel 2-cocycle using plethysms. Due
to Schur-Weyl duality we also need to employ the coproduct of the inner
multiplication. A detailed analysis including combinatorial proofs for our
results can be found in math-ph/0505037. In this paper we focus on the Hopf
algebraic treatment, and a more formal approach to representation rings and
symmetric functions.
