Theta对应下$K$ -型的宇称保持
Parity preservation of $K$-types under theta correspondence
摘要：
本文给出了$K$ -型在Howe θ对应下的度奇偶保持性。作为其应用，我们导出了任何李群的任意不可约$(\mathfrak{g},K)$-模在约化对偶对中的所有$K$ -型的宇称保持性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
