Geodesic
Parity Preservation of K-Types under the Theta Correspondence
Journal of Lie theory, Tome 28 (2018) no. 3, pp. 663-672
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This note shows a property of degree-parity preservation for K-types under Howe's theta correspondence. As its application, we deduce the preservation of parity of all K-types occurring in an arbitrary irreducible (g, K)-module of any Lie group in reductive dual pairs.
Classification : 22E46, 11F27
Mots-clés : Theta correspondence, reductive dual pair, Howe duality, K-type, degree, parity 
@article{JLT_2018_28_3_JLT_2018_28_3_a3,
     author = {X. Fan},
     title = {Parity {Preservation} of {K-Types} under the {Theta} {Correspondence}},
     journal = {Journal of Lie theory},
     pages = {663--672},
     year = {2018},
     volume = {28},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_3_JLT_2018_28_3_a3/}
}
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X. Fan. Parity Preservation of K-Types under the Theta Correspondence. Journal of Lie theory, Tome 28 (2018) no. 3, pp. 663-672. http://geodesic.mathdoc.fr/item/JLT_2018_28_3_JLT_2018_28_3_a3/