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Reciprocity theorems for the classical groups. I: The GL(r,k)-subgroup of GL(2r,k). (English) Zbl 0584.20031

Let \(\pi\) be an irreducible representation of GL(2r,k) and \(\tau\) an irreducible representation of a copy H of GL(r,k) in GL(2r,k). The main result of this paper gives necessary and sufficient conditions on the highest weights of \(\pi\) and \(\tau\) in order that the space of linear maps intertwining \(\tau\) and the restriction of \(\pi\) to H be naturally isomorphic to the space of all linear maps from the space of \(\tau\) to the space of \(\pi\).

MSC:

20G05 Representation theory for linear algebraic groups
20G15 Linear algebraic groups over arbitrary fields
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