Dual Banach algebras and Connes-amenability.
Let be a -adic field. Let be the group of -rational points of a connected reductive group defined over , and let be its Lie algebra. Under certain hypotheses on and , wequantifythe tempered dual of via the Plancherel formula on , using some character expansions. This involves matching spectral decomposition factors of the Plancherel formulas on and . As a consequence, we prove that any tempered representation contains a good minimal -type; we extend this result to irreducible...
We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair. For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in...
Un survol des conjectures de Drinfeld, Beilinson, Gaitsgory et al. et de résultats de Gaitsgory sur la correspondance de Langlands quantique.
A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.