Journal of Lie Theory

no. 1
A Simple Proof of the Algebraic Version of a Conjecture by Vogan
Journal of Lie Theory, Volume 18 (2008) no. 1, pp. 83-91
D. Vogan ["Unitary representations and complex analysis", Notes from the Cime summer school, Venice, Italy 2004] conjectured that four canonical globalizations of Harish-Chandra modules commute with certain n-cohomology groups. In this article we prove that Vogan's conjecture holds for one of the globalizations if and only if it holds for the dual. Using a previously published result of one of the authors, which establishes the conjecture for the minimal globalization, we can therefore deduce Vogan's conjecture for the maximal globalization.
DOI: 10.5802/jolt.483
Classification: 22E46
Keywords: Representations of reductive Lie groups, n-homology groups, globalizations of Harish-Chandra modules 
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     author = {T. Bratten and S. Corti},
     title = {A {Simple} {Proof} of the {Algebraic} {Version} of a {Conjecture} by {Vogan}},
     journal = {Journal of Lie Theory},
     pages = {83--91},
     year = {2008},
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     number = {1},
     doi = {10.5802/jolt.483},
     zbl = {1157.22006},
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T. Bratten; S. Corti. A Simple Proof of the Algebraic Version of a Conjecture by Vogan. Journal of Lie Theory, Volume 18 (2008) no. 1, pp. 83-91. doi: 10.5802/jolt.483

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