Some more exceptional numerology
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 19, Tome 375 (2010), pp. 22-31 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the present paper, we supply some additional details concerning parametrisation of the senior Weyl orbit of equations on the highest weight orbit in the adjoint representations of Chevalley groups of types $\mathrm E_7$ and $\mathrm E_8$, as given in my paper “Numerology of square equations”. Bibl. – 25 titles.
@article{ZNSL_2010_375_a1,
     author = {N. A. Vavilov},
     title = {Some more exceptional numerology},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {22--31},
     year = {2010},
     volume = {375},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a1/}
}
TY  - JOUR
AU  - N. A. Vavilov
TI  - Some more exceptional numerology
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2010
SP  - 22
EP  - 31
VL  - 375
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a1/
LA  - ru
ID  - ZNSL_2010_375_a1
ER  - 
%0 Journal Article
%A N. A. Vavilov
%T Some more exceptional numerology
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 22-31
%V 375
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a1/
%G ru
%F ZNSL_2010_375_a1
N. A. Vavilov. Some more exceptional numerology. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 19, Tome 375 (2010), pp. 22-31. http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a1/

[1] E. Abe, “Avtomorfizmy grupp Shevalle nad kommutativnymi koltsami”, Algebra i Analiz, 5:2 (1993), 74–90 | MR | Zbl

[2] E. I. Bunina, “Avtomorfizmy grupp Shevalle tipov $\mathrm A_l$, $\mathrm D_l$ i $\mathrm E_l$ nad lokalnymi koltsami s 1/2”, Fundam. Prikl. Mat., 15:2 (2009), 35–59

[3] E. I. Bunina, “Avtomorfizmy elementarnykh prisoedinennykh grupp Shevalle tipov $A_l$, $D_l$ i $E_l$ nad lokalnymi koltsami s 1/2”, Algebra i Logika, 48:4 (2009), 443–470 | MR | Zbl

[4] N. Burbaki, Gruppy i algebry Li, gl. IV–VI, M., 1972, 334 pp. | MR | Zbl

[5] N. Burbaki, Gruppy i algebry Li, gl. VII, VIII, Mir, M., 1978, 342 pp. | MR

[6] N. A. Vavilov, “Kak uvidet znaki strukturnykh konstant?”, Algebra i Analiz, 19:4 (2007), 34–68 | MR

[7] N. A. Vavilov, “Numerologiya kvadratnykh uravnenii”, Algebra i Analiz, 20:5 (2008), 9–40 | MR

[8] N. A. Vavilov, A. Yu. Luzgarev, “Normalizator gruppy Shevalle tipa $\mathrm E_6$”, Algebra i analiz, 19:5 (2007), 37–64 | MR

[9] 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

[10] N. A. Vavilov, N. P. Kharchev, “Orbity stabilizatora podsistem”, Zap. nauchn. semin. POMI, 338, 2006, 98–124 | MR | Zbl

[11] R. Karter, “Klassy sopryazhennykh elementov v gruppe Veilya”, Seminar po algebraicheskim gruppam, Mir, M., 1973, 288–306 | MR

[12] A. Yu. Luzgarev, “Uravneniya, opredelyayuschie orbitu starshego vesa v prisoedinennom predstavlenii”, Algebra i Analiz, 2010 (to appear)

[13] Yu. I. Manin, Kubicheskie formy: algebra, geometriya, arifmetika, Nauka, M., 1972, 1–29 | MR | Zbl

[14] M. Brion, V. Lakshmibai, “A geometric approach to standard monomial theory”, J. Representation Theory, 7 (2003), 651–680 | DOI | MR | Zbl

[15] R. W. Carter, “Conjugacy classes in the Weyl group”, Compositio Math., 25:1 (1972), 1–59 | MR | Zbl

[16] A. M. Cohen, R. H. Cushman, “Gröbner bases and standard monomial theory”, Computational Algebraic Geometry, Birkhäuser, Boston et al., 1993, 41–60 | DOI | MR | Zbl

[17] N. Gonciulea, V. Lakshmibai, Gröbner bases and standard monomial bases, 2001, 8 pp.

[18] A. Harebov, N. Vavilov, “On the lattice of subgroups of Chevalley groups containing a split maximal torus”, Comm. Algebra, 24:1 (1996), 109–133 | DOI | MR | Zbl

[19] V. Lakshmibai, P. Littelmann, P. Magyar, “Standard monomial theory and applications”, Representation Theory and Geometry, Kluwer Acad. Publ., Dordrecht et al., 1998, 319–364 | DOI | MR | Zbl

[20] V. Lakshmibai, C. S. Seshadri, “Standard monomial theory”, Hyderabad Conference on Algebraic Groups, Manoj Prakashan, Madras, 1991, 279–323 | MR

[21] A. Luzgarev, V. Petrov, N. Vavilov, “Explicit equations on orbit of the highest weight vector”, 2010 (to appear)

[22] E. Plotkin, A. Semenov, N. Vavilov, “Visual basic representations: an atlas”, Internat. J. Algebra and Comput., 8:1 (1998), 61–95 | DOI | MR | Zbl

[23] C. S. Seshadri, “Geometry of $G/P$. I. Standard monomial theory for minuscule $P$”, C. P. Ramanujam: a tribute, Tata Press, Bombay, 1978, 207–239 | MR | Zbl

[24] N. Vavilov, “A third look at weight diagrams”, Rendiconti del Rend. Sem. Mat. Univ. Padova, 204:1 (2000), 201–250 | MR

[25] N. A. Vavilov, “Do it yourself structure constants for Lie algebras of type $\mathrm E_l$”, Zap. nauchn. semin. POMI, 281, 2001, 60–104 | MR | Zbl