On donne une description de la restriction des modules de à , où est considéré comme sous-groupe par l’action sur les formes binaires cubiques. On obtient une formule numérique pour les multiplicités, et un ensemble minimal de générateurs pour la réalisation géométrique naturelle de cette formule.
We describe the branching rule from to , where the latter is embedded via its action on binary cubic forms. We obtain both a numerical multiplicity formula, as well as a minimal system of generators for the geometric realization of the rule.
@article{AIF_1998__48_1_29_0, author = {Papageorgiou, Yannis Y.}, title = {$SL_2$, the cubic and the quartic}, journal = {Annales de l'Institut Fourier}, pages = {29--71}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {1}, year = {1998}, doi = {10.5802/aif.1610}, zbl = {0901.20030}, mrnumber = {99f:20071}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1610/} }
TY - JOUR AU - Papageorgiou, Yannis Y. TI - $SL_2$, the cubic and the quartic JO - Annales de l'Institut Fourier PY - 1998 SP - 29 EP - 71 VL - 48 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1610/ DO - 10.5802/aif.1610 LA - en ID - AIF_1998__48_1_29_0 ER -
%0 Journal Article %A Papageorgiou, Yannis Y. %T $SL_2$, the cubic and the quartic %J Annales de l'Institut Fourier %D 1998 %P 29-71 %V 48 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1610/ %R 10.5802/aif.1610 %G en %F AIF_1998__48_1_29_0
Papageorgiou, Yannis Y. $SL_2$, the cubic and the quartic. Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 29-71. doi : 10.5802/aif.1610. https://aif.centre-mersenne.org/articles/10.5802/aif.1610/
[Br] Représentations exceptionnelles des groupes semi-simples, Ann. Scient. Éc. Norm. Sup., 4e série, 18 (1985), 345-387. | Numdam | MR | Zbl
,[G] Die simultanen Systeme binärer Formen, Math. Ann., 2 (1870), 227-280. | JFM
,[GI] Vorlesungen über Invarianten Theorie, reprinted by Chelsea Publishing Co., New York, 1987.
,[Gu] Zur Theorie des simultanen Systems einer cubischen und einer biquadratischen binären Form, J.B. Metzler, Stuttgart, 1869. | JFM
,[H-Per] Perspectives on invariant theory: Schur duality, multiplicity-free actions, and beyond, Isr. Math. Conf. Proc., 8 (1995), 1-182. | MR | Zbl
,[H-Rem] Remarks on classical invariant theory, Trans. Amer. Math. Soc., 313 (1989), 539-570. | MR | Zbl
,[HU] The Capelli identity, the double commutant theorem and multiplicity-free actions, Math. Ann., 290 (1991), 565-619. | Zbl
and ,[Hum] Introduction to Lie Algebras and Representation Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1972. | MR | Zbl
,[KKLV] Algebraic Transformation Groups and Invariant Theory (H. Kraft et al., eds), Birkhäuser Basel Boston Berlin, 1989, 63-76. | Zbl
et .,[KT] Young-Diagrammatic Methods for the Representation Theory of the Classical Groups of type Bn, Cn and Dn, J. Alg., 107 (1987), 466-511. | MR | Zbl
and ,[K] A formula for the Multiplicity of a Weight, Trans. Amer. Math. Soc., 93 (1959), 53-73. | MR | Zbl
,[LP1] A Generalization of the Littlewood-Richardson Rule, J. Alg., 130 (1990), 328-368. | MR | Zbl
,[LP2] A Littlewood-Richardson Rule for Symmetrizable Kac-Moody Algebras, Invent. Math., 116 (1994), 329-346. | MR | Zbl
,[LDE] On Invariants under Restricted Groups, Philos. Trans. Roy. Soc. A, 239 (1944), 387-417. | MR | Zbl
,[M] Bericht über den gegenwärtigen Stand der Invariantentheorie, Jahresbericht der DMV, Band 1 (1892), 79-292. | JFM
,[S] Lessons Introductory to the Higher Modern Algebra, Hodges, Figgis, and Co., 1885.
,[Sch] On classical invariant theory and binary cubics, Ann. Inst. Fourier, 37-3 (1987), 191-216. | Numdam | MR | Zbl
,[Sp] Invariant Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1977. | MR | Zbl
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