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Journal of Lie Theory 28 (2018), No. 3, 663--672
Copyright Heldermann Verlag 2018

Parity Preservation of K-Types under the Theta Correspondence

Xiang Fan
School of Mathematics, Sun Yat-sen University, Guangzhou 510275, P. R. China

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.

Keywords: Theta correspondence, reductive dual pair, Howe duality, K-type, degree, parity.

MSC: 22E46, 11F27

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