Journal of Lie Theory

no. 3
Parity Preservation of K-Types under the Theta Correspondence
Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 663-672
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.
DOI: 10.5802/jolt.1019
Classification: 22E46, 11F27
Keywords: Theta correspondence, reductive dual pair, Howe duality, K-type, degree, parity 
@article{JOLT_2018_28_3_a3,
     author = {X. Fan},
     title = {Parity {Preservation} of {K-Types} under the {Theta} {Correspondence}},
     journal = {Journal of Lie Theory},
     pages = {663--672},
     year = {2018},
     volume = {28},
     number = {3},
     doi = {10.5802/jolt.1019},
     zbl = {1395.22004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1019/}
}
TY  - JOUR
AU  - X. Fan
TI  - Parity Preservation of K-Types under the Theta Correspondence
JO  - Journal of Lie Theory
PY  - 2018
SP  - 663
EP  - 672
VL  - 28
IS  - 3
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1019/
DO  - 10.5802/jolt.1019
ID  - JOLT_2018_28_3_a3
ER  - 
%0 Journal Article
%A X. Fan
%T Parity Preservation of K-Types under the Theta Correspondence
%J Journal of Lie Theory
%D 2018
%P 663-672
%V 28
%N 3
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1019/
%R 10.5802/jolt.1019
%F JOLT_2018_28_3_a3
X. Fan. Parity Preservation of K-Types under the Theta Correspondence. Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 663-672. doi: 10.5802/jolt.1019

Cited by Sources: