# On subgroups of the orthogonal group

@article{Obata1958OnSO, title={On subgroups of the orthogonal group}, author={Morio Obata}, journal={Transactions of the American Mathematical Society}, year={1958}, volume={87}, pages={347-358} }

with a finite number of exceptions for the values of re. But it has not yet been made clear what values of re are exceptional. This note will give an answer to the analogous problem for a wider interval of the dimension of G. In §1 we shall explain some notations and then, in §2, a relation between irreducibility and absolute irreducibility will be discussed; especially a condition for a representation to be unitary symplectic will be given. In §3 we shall obtain inequalities concerning the… Expand

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