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Parity preservation of $K$-types under theta correspondence
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classification
math.RT
keywords
preservationtypescorrespondenceparitythetaunderapplicationarbitrary
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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