Geodesic
Orbits of vectors in some representations. III
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 39, Tome 522 (2023), pp. 152-163 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $\Phi$ be a root system of type $E_6$, $E_7$, or $E_8$. Let $K$ be a field of characteristic $2$. Let $\delta$ be the maximal root of $\Phi$ and set $\Phi_0 = \{\alpha\in\Phi; \delta\perp\alpha\}$. The orbits of the group $G_{\mathrm sc}(\Phi_0, K)$ acting on the set $\langle e_\alpha; \angle(\alpha, \delta) = \pi/3\rangle$ are described. 
@article{ZNSL_2023_522_a8,
     author = {I. M. Pevzner},
     title = {Orbits of vectors in some representations. {III}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {152--163},
     year = {2023},
     volume = {522},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a8/}
}
TY  - JOUR
AU  - I. M. Pevzner
TI  - Orbits of vectors in some representations. III
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 152
EP  - 163
VL  - 522
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a8/
LA  - ru
ID  - ZNSL_2023_522_a8
ER  - 
%0 Journal Article
%A I. M. Pevzner
%T Orbits of vectors in some representations. III
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 152-163
%V 522
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a8/
%G ru
%F ZNSL_2023_522_a8
I. M. Pevzner. Orbits of vectors in some representations. III. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 39, Tome 522 (2023), pp. 152-163. http://geodesic.mathdoc.fr/item/ZNSL_2023_522_a8/

[1] A. Borel, “Svoistva i lineinye predstavleniya grupp Shevalle”, Seminar po algebraicheskim gruppam, Mir, M., 1973, 9–59

[2] N. Burbaki, Gruppy i algebry Li, Glavy IV–VI, Mir, M., 1972 | MR

[3] N. Burbaki, Gruppy i algebry Li, Glavy VII–VIII, Mir, M., 1978 | MR

[4] N. A. Vavilov, A. Yu. Luzgarev, “Normalizator gruppy Shevalle tipa $\mathrm{E}_7$”, Algebra i analiz, 27:6 (2015), 57–88

[5] N. A. Vavilov, A. Yu. Luzgarev, I. M. Pevzner, “Gruppa Shevalle tipa $\mathrm{E}_6$ v $27$-mernom predstavlenii”, Zap. nauchn. semin. POMI, 338, 2006, 5–68 | MR | Zbl

[6] N. A. Vavilov, I. M. Pevzner, “Troiki dlinnykh kornevykh podgrupp”, Zap. nauchn. semin. POMI, 343, 2007, 54–83

[7] N. A. Vavilov, A. A. Semenov, “Dlinnye kornevye tory v gruppakh Shevalle”, Algebra i analiz, 24:3 (2012), 22–83

[8] A. Yu. Luzgarev, “Ne zavisyaschie ot kharakteristiki invarianty chetvertoi stepeni dlya $G(\mathrm{E}_7,R)$”, Vestnik Sankt-Peterburgskogo universiteta. Seriya 1: matematika, mekhanika, astronomiya, 2013, no. 1, 43–50 | MR

[9] A. Yu. Luzgarev, I. M. Pevzner, “Nekotorye fakty iz zhizni $\mathrm{GL}(5,\mathbb{Z})$”, Zap. nauchn. semin. POMI, 305, 2003, 153–163

[10] O. O'Mira, “Avtomorfizmy klassicheskikh grupp”, Lektsii o lineinykh gruppakh, Mir, M., 1976, 57–167

[11] O. O'Mira, Lektsii o simplekticheskikh gruppakh, Mir, M., 1979

[12] I. M. Pevzner, “Geometriya kornevykh elementov v gruppakh tipa $\mathrm{E}_6$”, Algebra i analiz, 23:3 (2011), 261–309

[13] I. M. Pevzner, “Shirina grupp tipa $\mathrm{E}_{6}$ otnositelno mnozhestva kornevykh elementov, I”, Algebra i analiz, 23:5 (2011), 155–198

[14] I. M. Pevzner, “Shirina grupp tipa $\mathrm{E}_{6}$ otnositelno mnozhestva kornevykh elementov, II”, Zap. nauchn. semin. POMI, 386, 2011, 242–264

[15] I. M. Pevzner, “Shirina gruppy $\mathrm{GL}(6,K)$ otnositelno mnozhestva kvazikornevykh elementov”, Zap. nauchn. semin. POMI, 423, 2014, 183–204

[16] I. M. Pevzner, “Shirina ekstraspetsialnogo unipotentnogo radikala otnositelno mnozhestva kornevykh elementov”, Zap. nauchn. semin. POMI, 435, 2015, 168–177

[17] I. M. Pevzner, “Suschestvovanie kornevoi podgruppy, kotoruyu dannyi element perevodit v protivopolozhnuyu”, Zap. nauchn. semin. POMI, 460, 2017, 190–202

[18] I. M. Pevzner, “Orbity vektorov nekotorykh predstavlenii. I”, Zap. nauchn. semin. POMI, 484 (2019), 149–164

[19] I. M. Pevzner, “Orbity vektorov nekotorykh predstavlenii. II”, Zap. nauchn. semin. POMI, 522

[20] T. A. Springer, “Lineinye algebraicheskie gruppy”, Algebraicheskaya geometriya – 4, Itogi nauki i tekhn. Ser. Sovrem. problemy mat. Fundam. napravleniya, 55, VINITI, M., 1989, 5–136

[21] R. Steinberg, Lektsii o gruppakh Shevalle, Mir, M., 1975

[22] Dzh. Khamfri, Lineinye algebraicheskie gruppy, Nauka, M., 1980

[23] Dzh. Khamfri, Vvedenie v teoriyu algebr Li i ikh predstavlenii, MTsNMO, M., 2003

[24] M. Aschbacher, “The 27-dimensional module for $E_6$. I”, Invent. Math., 89:1 (1987), 159–195 | DOI | MR | Zbl

[25] M. Aschbacher, “The 27-dimensional module for $E_6$. II”, J. London Math. Soc, 37 (1988), 275–293 | DOI | MR | Zbl

[26] M. Aschbacher, “The 27-dimensional module for $E_6$. III”, Trans. Amer. Math. Soc., 321 (1990), 45–84 | MR | Zbl

[27] M. Aschbacher, “The 27-dimensional module for $E_6$. IV”, J. Algebra, 131 (1990), 23–39 | DOI | MR | Zbl

[28] M. Aschbacher, “Some multilinear forms with large isometry groups”, Geom. Dedicata, 25:1–3 (1988), 417–465 | MR

[29] M. Aschbacher, “The geometry of trilinear forms”, Finite Geometries, Buildings and Related topics, Oxford Univ. Press, Oxford, 1990, 75–84 | DOI | MR

[30] B. N. Cooperstein, “The fifty-six-dimensional module for $E_7$. I. A four form for $E_7$”, J. Algebra, 173:2 (1995), 361–389 | DOI | MR | Zbl

[31] S. Krutelevich, “Jordan algebras, exceptional groups, and Bhargava composition”, J. Algebra, 314:2 (2007), 924–977 | DOI | MR | Zbl

[32] T. A. Springer, Linear algebraic groups, Progress in Mathematics, 9, Birkhäuser Boston Inc., Boston, 1998 | MR | Zbl

[33] J. Tits, “Sur les constantes de structure et le thèorème d'existence des algèbres de Lie semi-simples”, Inst. Hautes Études Sci. Publ. Math., 1966, no. 31, 21–58 | DOI | MR

[34] N. A. Vavilov, “A third look at weight diagrams”, Rend. Sem. Mat. Univ. Padova, 104 (2000), 201–250 | MR | Zbl

[35] N. A. Vavilov, E. B. Plotkin, “Chevalley groups over commutative rings. I. Elementary calculations”, Acta Applicandae Math., 45 (1996), 73–115 | DOI | MR