Parity preservation of $K$-types under theta correspondence

Xiang Fan

Parity preservation of $K$-types under theta correspondence

Representation Theory 2018-12-07 v2

Authors: Xiang Fan

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.

Keywords

theta correspondence K-types parity preservation Howe correspondence irreducible ($\mathfrak{g},K$)-modules reductive dual pairs

Cite

@article{arxiv.1603.09673,
  title  = {Parity preservation of $K$-types under theta correspondence},
  author = {Xiang Fan},
  journal= {arXiv preprint arXiv:1603.09673},
  year   = {2018}
}

Comments

8 pages

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