Journal of Lie Theory

no. 4
Noncubic Dirac Operators for Finite-Dimensional Modules
Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 1113-1140
We study the decomposition into irreducibles of the kernel of noncubic Dirac operators attached to finite-dimensional modules. We compare this decomposition with features of Kostant's cubic Dirac operator. In particular, we show that the kernel of noncubic Dirac operators need not contain full isotypic components. The cases of classical and exceptional complex Lie algebras are studied in details. As a by-product, we deduce some information on the kernel of noncubic geometric Dirac operators acting on sections over compact manifolds studied by Slebarski.
DOI: 10.5802/jolt.1214
Classification: 17B45, 20G05
Keywords: Complex semisimple Lie algebras, highest weight representations, Dirac operators, Dirac cohomology, Weyl inequalities 
@article{JOLT_2021_31_4_a14,
     author = {S. Afentoulidis-Almpanis},
     title = {Noncubic {Dirac} {Operators} for {Finite-Dimensional} {Modules}},
     journal = {Journal of Lie Theory},
     pages = {1113--1140},
     year = {2021},
     volume = {31},
     number = {4},
     doi = {10.5802/jolt.1214},
     zbl = {1497.17026},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1214/}
}
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S. Afentoulidis-Almpanis. Noncubic Dirac Operators for Finite-Dimensional Modules. Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 1113-1140. doi: 10.5802/jolt.1214

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