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Dual Blobs and Plancherel Formulas

Ju-Lee Kim (2004)

Bulletin de la Société Mathématique de France

Let k be a p -adic field. Let G be the group of k -rational points of a connected reductive group 𝖦 defined over k , and let 𝔤 be its Lie algebra. Under certain hypotheses on 𝖦 and k , wequantifythe tempered dual G ^ of G via the Plancherel formula on 𝔤 , using some character expansions. This involves matching spectral decomposition factors of the Plancherel formulas on 𝔤 and G . As a consequence, we prove that any tempered representation contains a good minimal 𝖪 -type; we extend this result to irreducible...

Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

Andrzej Daszkiewicz, Witold Kraśkiewicz, Tomasz Przebinda (2005)

Open Mathematics

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...

Dualité de Langlands quantique

Vadim Schechtman (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Un survol des conjectures de Drinfeld, Beilinson, Gaitsgory et al. et de résultats de Gaitsgory sur la correspondance de Langlands quantique.

Duality of Hodge numbers of compact complex nilmanifolds

Takumi Yamada (2015)

Complex Manifolds

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.

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