Geodesic
Noncubic Dirac Operators for Finite-Dimensional Modules
Spyridon Afentoulidis-Almpanis1
1Faculty of Mathematics, University of Lorraine, Metz, France
Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1113-1140

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B45, 20G05
Mots-clés : Complex semisimple Lie algebras, highest weight representations, Dirac operators, Dirac cohomology, Weyl inequalities

Spyridon Afentoulidis-Almpanis  1

1 Faculty of Mathematics, University of Lorraine, Metz, France 
Spyridon Afentoulidis-Almpanis. Noncubic Dirac Operators for Finite-Dimensional Modules. Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1113-1140. http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a14/
@article{JOLT_2021_31_4_a14,
     author = {Spyridon Afentoulidis-Almpanis},
     title = {Noncubic {Dirac} {Operators} for {Finite-Dimensional} {Modules}},
     journal = {Journal of Lie Theory},
     pages = {1113--1140},
     year = {2021},
     volume = {31},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a14/}
}
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