Branching problems of Zuckerman derived functor modules

Abstract

We discuss recent developments on branching problems of irreducible unitary representations $\pi$ of real reductive groups when restricted to reductive subgroups. Highlighting the case where the underlying $(g,K)$-modules of $\pi$ are isomorphic to Zuckerman's derived functor modules $A_q(\lambda )$, 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.

Proceedings of Conference in honor of Gregg Zuckerman's 60th birthday at Yale in 2009 (v3: fixed 3 typos)

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