Geodesic
On Harmonic Polynomials Invariant under Unitary Transformations
Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 856-871

Voir la notice de l'article provenant de la source Math-Net.Ru

Unitary transformations and canonical representatives of a family of real-valued harmonic fourth-degree polynomials in three complex variables are studied. The subject relates to the study of Moser normal equations for real hypersurfaces of four-dimensional complex spaces and isotropy groups (holomorphic stabilizers) of such surfaces. The dimension of the stabilizer for a particular strictly pseudo-convex hypersurface is estimated from above by the dimension of a unitary subgroup preserving the fourth-degree polynomial from its normal equation.
Keywords: unitary transformation, Lie algebra, harmonic function, homogeneous polynomial.
Mots-clés : group invariant 
@article{MZM_2021_109_6_a5,
     author = {A. V. Loboda and B. M. Darinskii and D. V. Kozoriz},
     title = {On {Harmonic} {Polynomials} {Invariant} under {Unitary} {Transformations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {856--871},
     publisher = {mathdoc},
     volume = {109},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a5/}
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A. V. Loboda; B. M. Darinskii; D. V. Kozoriz. On Harmonic Polynomials Invariant under Unitary Transformations. Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 856-871. http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a5/