On the canonical \(k\)-types in the irreducible unitary \(\mathfrak g\)-modules with non-zero relative cohomology
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Publication:1143508
DOI10.1007/BF01390311zbMath0442.22010MaRDI QIDQ1143508
Publication date: 1980
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/142726
highest weightCartan decompositionvanishing theoremsrelative cohomologyirreducible unitary g-modulesirreducible, unitary representationnoncompact real form of \(G_2\)
Semisimple Lie groups and their representations (22E46) Connections of group theory with homological algebra and category theory (20J99)
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Classification of discrete series by minimal 𝐾-type ⋮ Stable base change C/R of certain derived functor modules ⋮ Unnamed Item ⋮ On the unitary dual of the classical Lie groups, representations of $Sp(p,q)$ ⋮ Restriction of the holomorphic cohomology of a Shimura variety to a smaller Shimura variety. ⋮ On the unitary dual of real reductive Lie groups and the \(A_g(\lambda)\) modules: The strongly regular case ⋮ Dirac cohomology, unitary representations and a proof of a conjecture of Vogan ⋮ Low degree cohomologies of congruence groups ⋮ Representation theoretic harmonic spinors for coherent families ⋮ Vanishing on cohomology associated to Hermitian symmetric spaces ⋮ Lie algebra cohomology and the resolution of certain Harish-Chandra modules ⋮ An inequality among infinitesimal characters related to the lowest \(K\)-types of discrete series ⋮ Restriction of the cohomology of a Shimura variety to its subvarieties ⋮ Residues of Eisenstein series and the automorphic cohomology of reductive groups ⋮ The Modularity of Special Cycles on Orthogonal Shimura Varieties over Totally Real Fields under the Beilinson–Bloch Conjecture
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