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 modulesA_{q}(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