Various forms of invariant tensor products appeared in the literature implicitly, for example, in Schur’s orthogonality for finite groups. In many cases, they are employed to study the space HomG(π1, π2) where one of the representations π1 and π2 is irreducible. In this paper, we formulate the concept of invariant tensor product uniformly. We also study the invariant tensor functor associated with discrete series representations for classical groups. For motivations and applications.
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