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A simple question about a complicated object

Pierre-Yves Gaillard
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Abstract

Let n and k be positive integers with and k < n. Then of course SU(k,1) is contained into SU(n,1). Moreover, which is less clear - but proved by Khoroshkin -, the representation theory of SU(k,1) at the generalized infinitesimal character of the trivial module can be fully (and even Ext-fully) embedded into that of SU(n,1). Here is the obvious bet: This embedding is implemented by the cohomological induction functor. I conjecture that a similar phenomenon occurs whenever SU(k,1) is a Levi factor of a theta stable parabolic subalgebra of a reductive group.

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Pierre-Yves Gaillard. 2009-07-22. A simple question about a complicated object. https://arxiv.org/abs/math/0003183

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