@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/}
}
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