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arXiv · 1603.09673

Parity preservation of $K$-types under theta correspondence

Xiang Fan
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Abstract

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 $(\mathfrak{g},K)$-module of any Lie group in reductive dual pairs.

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Xiang Fan. 2016-03-31. Parity preservation of $K$-types under theta correspondence. https://arxiv.org/abs/1603.09673

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