Inductive systems of representations with small highest weights for~natural embeddings of symplectic groups

A. A. Osinovskaya ; I. D. Suprunenko

Trudy Instituta matematiki, Tome 22 (2014) no. 2, pp. 109-118

Résumé

For natural embeddings of symplectic groups, inductive systems of irreducible representations where the maximum of the highest weight value on the maximal root is equal to $2$ are studied. For such embeddings of algebraic groups of type $C_n$ in characteristic $3$, the inductive system of representations generated by irreducible representations with highest weight $2\omega_n$ is determined. It is proved that any inductive system of representations of such groups consisting of representations with the value of the highest weight on the maximal root at most $2$ and containing representations with such value equal to $2$ contains the subsystem generated by the standard representations or the subsystem generated by the representations with highest weight $\omega_n$, For algebraic groups of type $C_n$ in characteristic $3$, the restrictions of certain irreducible modules to subsystem subgroups of type $C_{n-1}$ are described.