T. Kobayashi, Branching problems of Zuckerman derived functor modules, Representation Theory and Mathematical Physics (in honor of Gregg Zuckerman) (Jeffrey Adams, Bong Lian, and Siddhartha Sahi, eds.), Contemporary Mathematics, vol. 557, Amer. Math. Soc., Providence, RI, 2011, pp. 23-40, ISBNF 9780821852460. arXiv:1104.4399..
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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