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/}
}
TY  - JOUR
AU  - A. V. Loboda
AU  - B. M. Darinskii
AU  - D. V. Kozoriz
TI  - On Harmonic Polynomials Invariant under Unitary Transformations
JO  - Matematičeskie zametki
PY  - 2021
SP  - 856
EP  - 871
VL  - 109
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a5/
LA  - ru
ID  - MZM_2021_109_6_a5
ER  - 
%0 Journal Article
%A A. V. Loboda
%A B. M. Darinskii
%A D. V. Kozoriz
%T On Harmonic Polynomials Invariant under Unitary Transformations
%J Matematičeskie zametki
%D 2021
%P 856-871
%V 109
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a5/
%G ru
%F MZM_2021_109_6_a5
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/

[1] S. S. Chern, J. K. Moser, “Real hypersurfaces in complex manifolds”, Acta Math., 133 (1974), 219–271 | DOI | MR

[2] V. V. Ezhov, A. V. Loboda, G. Shmalts, “Kanonicheskaya forma mnogochlena chetvertoi stepeni v normalnom uravnenii veschestvennoi giperpoverkhnosti v $\mathbb C^3$”, Matem. zametki, 66:4 (1999), 624–626 | DOI | MR

[3] A. V. Loboda, “O razmernosti gruppy, tranzitivno deistvuyuschei na giperpoverkhnosti v $\mathbb{C}^3$”, Funkts. analiz i ego pril., 33:1 (1999), 68–71 | DOI | MR | Zbl

[4] A. V. Atanov, A. V. Loboda, “Ob orbitakh odnoi nerazreshimoi $5$-mernoi algebry Li”, Matem. fiz. i komp. model., 22:2 (2019), 5–20 | DOI

[5] A. G. Vitushkin, “Golomorfnye otobrazheniya i geometriya poverkhnostei”, Kompleksnyi analiz – mnogie peremennye – 1, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 7, VINITI, M., 1985, 167–226 | MR | Zbl

[6] Yu. G. Borisovich, B. M. Darinskii, O. V. Kunakovskaya, “Primenenie topologicheskikh metodov dlya otsenki chisla prodolnykh uprugikh voln v kristallakh”, TMF, 94:1 (1993), 146–152 | MR | Zbl

[7] Z. I. Borevich, S. L. Krupetskii, “Podgruppy unitarnoi gruppy, soderzhaschie gruppu diagonalnykh matrits”, Algebraicheskie chisla i konechnye gruppy, Zap. nauchn. sem. LOMI, 86, Izd-vo «Nauka», Leningrad. otd., L., 1979, 19–29 | MR | Zbl

[8] A. V. Isaev, “On Chern–Moser normal forms of strongly pseudoconvex hypersurfaces with high-dimensional stability group”, Pacific J. Math., 235:2 (2008), 235–244 | DOI | MR

[9] B. Kruglikov, “Submaximally symmetric CR-structures”, J. Geom. Anal., 26:4 (2015), 3090–3097 | DOI | MR