On irreducible algebras of conformal endomorphisms over a linear algebraic group

We study the algebra of conformal endomorphisms ${\text{Cend}}_n^{G,G}$ of a finitely generated free module $M_n$ over the coordinate Hopf algebra $H$ of a linear algebraic group $G$. It is shown that a conformal subalgebra of ${\text{Cend}}_n$ acting irreducibly on $M_n$ generates an essential left ideal of ${\text{Cend}}_n^{G,G}$ if enriched with operators of multiplication on elements of $H$. In particular, we describe such subalgebras for the case when $G$ is finite.