Geodesic
PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS
Glasgow mathematical journal, Tome 62 (2020) no. 2, pp. 355-366

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we consider parabolic subroot systems of a complex simple Lie Algebra. We describe root theoretic data of the subroot systems in terms of that of the root system and we give a selection of applications of our results to the study of generalized flag manifolds. 
BURNS, JOHN M.; MAKROONI, MOHAMMAD A. PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS. Glasgow mathematical journal, Tome 62 (2020) no. 2, pp. 355-366. doi: 10.1017/S0017089519000156
@article{10_1017_S0017089519000156,
     author = {BURNS, JOHN M. and MAKROONI, MOHAMMAD A.},
     title = {PARABOLIC {SUBROOT} {SYSTEMS} {AND} {THEIR} {APPLICATIONS}},
     journal = {Glasgow mathematical journal},
     pages = {355--366},
     year = {2020},
     volume = {62},
     number = {2},
     doi = {10.1017/S0017089519000156},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000156/}
}
TY  - JOUR
AU  - BURNS, JOHN M.
AU  - MAKROONI, MOHAMMAD A.
TI  - PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS
JO  - Glasgow mathematical journal
PY  - 2020
SP  - 355
EP  - 366
VL  - 62
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000156/
DO  - 10.1017/S0017089519000156
ID  - 10_1017_S0017089519000156
ER  - 
%0 Journal Article
%A BURNS, JOHN M.
%A MAKROONI, MOHAMMAD A.
%T PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS
%J Glasgow mathematical journal
%D 2020
%P 355-366
%V 62
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000156/
%R 10.1017/S0017089519000156
%F 10_1017_S0017089519000156

[1] Akhiezer, D. N., Lie group actions in complex analysis, Aspects of Mathematics, E27, (Friedr. Vieweg & Sohn, Braunschweig, 1995). Google Scholar | DOI

[2] Alekseevsky, D. V. and Perelomov, A. M., Invariant Kähler-Einstein metrics on compact homogeneous spaces, Funct. Anal. Appl. 20 (1986), 171–182. Google Scholar

[3] Arvanitoyeorgos, A. and Chrysikos, I., Invariant Einstein metrics on flag manifolds with four isotropy summands, Ann. Global Anal. Geom. 37(2) (2010), 185–219.10.1007/s10455-009-9183-7 Google Scholar | DOI

[4] Beltrametti, M. C., Fania, M. L. and Sommese, A. J., On the discriminant variety of a projective manifold, Forum Math. 4(6) (1992), 529–547. Google Scholar

[5] Borel, A., On the curvature tensor of the Hermitian symmetric manifolds, Ann. Math. 71(2) (1960), 508–521.10.2307/1969940 Google Scholar | DOI

[6] Borel, A. and De Siebenthal, J., Les sous-groupes fermés de rang maximum des groupes de Lie clos, Comment. Math. Helv. 23 (1949), 200–221. Google Scholar

[7] Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces. I, Am. J. Math. 80 (1958), 458–538. Google Scholar

[8] Bourbaki, N., Group et algèbres de Lie. Ch. 4, 5 et 6, (Hermann, Paris, 1968). Google Scholar

[9] Burns, J. M. and Clancy, M. J., Weight sum formulae in Lie algebra representations, J. Algebra 257(1) (2002), 1–12. Google Scholar

[10] Burns, J. M. and Clancy, M. J., Recurrence relations, Dynkin diagrams and Plcker formulae, Glasg. Math. J. 49(1) (2007), 53–59. Google Scholar

[11] Burns, J. M. and Makrooni, M. A., Compact homogeneous spaces with positive Euler characteristic and their ‘Strange Formula’, Quart. J. Math. 66 (2015), 507–516.10.1093/qmath/hav009 Google Scholar | DOI

[12] Carles, R., Méthode récurrente pour la classification des systèmes de racines réduits et irréductibles, C. R. Acad. Sci. Paris Sér, A–B 276 (1973), A355–A358. Google Scholar

[13] Carles, R., Dimensions des représentations fondamentales des algébres de Lie de type G , F , E , E , E , C. R. Acad. Sci. Paris Sér. A–B 276 (1973), A451–A453. Google Scholar

[14] Cellini, P. and Marietti, M., Root polytopes and Borel subalgebras, Int. Res. Not. 12(12) (2015), 4392–4420. Google Scholar

[15] Chen, B. Y. and Nagano, T., Totally geodesic submanifolds of symmetric spaces. II, Duke Math. J. 45(2) (1978), 405–425. Google Scholar

[16] Fino, A. and Salamon, S. M., Observations on the topology of symmetric spaces. Geometry and physics (Aarhus, 1995), Lecture Notes in Pure and Appl. Math., vol. 184, (Dekker, New York, 1997), 275–286. Google Scholar

[17] Helgason, S., Differential geometry, Lie groups, and symmetric spaces, (Academic Press, New York, 1978). Google Scholar

[18] Knop, F. and Menzel, G., Duale Varietten von Fahnenvarietten, Comment. Math. Helv. 62(1) (1987), 38–61.10.1007/BF02564437 Google Scholar | DOI

[19] Macdonald, I. G., Affine root systems and Dedekind’s η-function, Invent. Math. 15 (1972), 91–143 Google Scholar | DOI

[20] Quast, P., Centrioles in symmetric spaces, Nagoya Math. J. 211 (2013), 51–77. Google Scholar | DOI

[21] Snow, D. M., The nef value and defect of homogeneous line bundles, Trans. Am. Math. Soc. 340(1) (1993), 227–241.10.1090/S0002-9947-1993-1144015-8 Google Scholar | DOI

[22] Snow, D. M., Nef value of homogeneous line bundles and related vanishing theorems, Forum Math. 7(3) (1995), 385–392.10.1515/form.1995.7.385 Google Scholar | DOI

[23] Suter, R., Coxeter and dual Coxeter numbers, Comm. Algebra 26(1) (1998), 147–153. Google Scholar | DOI

[24] Tamaru, H., On certain subalgebras of graded Lie algebras, YokohamaMath. J. 46(2) (1999), 127–138. Google Scholar

[25] Wolf, J. A., Spaces of Constant Curvature, 5th edn., (Publish or Perish Inc., Wilmington, DE, 1984). Google Scholar

Cité par Sources :