We discuss recent developments on branching problems of irreducible unitary representations π of real reductive groups when restricted to reductive subgroups. Highlighting the case where the underlying (g,K)-modules of π are isomorphic to Zuckerman's derived functor modules Aq(λ), we show various and rich features of branching laws such as infinite multiplicities, irreducible restrictions, multiplicity-free restrictions, and discrete decomposable restrictions. We also formulate a number of conjectures.
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© Toshiyuki Kobayashi