no. 1
SL 2 , the cubic and the quartic
Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 29-71

We describe the branching rule from Sp 4 to SL 2 , 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.

On donne une description de la restriction des modules de Sp 4 à SL 2 , où SL 2 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.

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     title = {$SL_2$, the cubic and the quartic},
     journal = {Annales de l'Institut Fourier},
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     year = {1998},
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     doi = {10.5802/aif.1610},
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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

[Br] M. Brion, Représentations exceptionnelles des groupes semi-simples, Ann. Scient. Éc. Norm. Sup., 4e série, 18 (1985), 345-387. | Zbl | MR | Numdam

[G] P. Gordan, Die simultanen Systeme binärer Formen, Math. Ann., 2 (1870), 227-280. | JFM

[GI] P. Gordan, Vorlesungen über Invarianten Theorie, reprinted by Chelsea Publishing Co., New York, 1987.

[Gu] S. Gundelfinger, Zur Theorie des simultanen Systems einer cubischen und einer biquadratischen binären Form, J.B. Metzler, Stuttgart, 1869. | JFM

[H-Per] R. Howe, Perspectives on invariant theory: Schur duality, multiplicity-free actions, and beyond, Isr. Math. Conf. Proc., 8 (1995), 1-182. | Zbl | MR

[H-Rem] R. Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc., 313 (1989), 539-570. | Zbl | MR

[HU] R. Howe and T. Umeda, The Capelli identity, the double commutant theorem and multiplicity-free actions, Math. Ann., 290 (1991), 565-619. | Zbl

[Hum] J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1972. | Zbl | MR

[KKLV] F. Knop et Al., Algebraic Transformation Groups and Invariant Theory (H. Kraft et al., eds), Birkhäuser Basel Boston Berlin, 1989, 63-76. | Zbl

[KT] K. Koike and I. Terada, Young-Diagrammatic Methods for the Representation Theory of the Classical Groups of type Bn, Cn and Dn, J. Alg., 107 (1987), 466-511. | Zbl | MR

[K] B. Kostant, A formula for the Multiplicity of a Weight, Trans. Amer. Math. Soc., 93 (1959), 53-73. | Zbl | MR

[LP1] P. Littelmann, A Generalization of the Littlewood-Richardson Rule, J. Alg., 130 (1990), 328-368. | Zbl | MR

[LP2] P. Littelmann, A Littlewood-Richardson Rule for Symmetrizable Kac-Moody Algebras, Invent. Math., 116 (1994), 329-346. | Zbl | MR

[LDE] D.E. Littlewood, On Invariants under Restricted Groups, Philos. Trans. Roy. Soc. A, 239 (1944), 387-417. | Zbl | MR

[M] F. Meyer, Bericht über den gegenwärtigen Stand der Invariantentheorie, Jahresbericht der DMV, Band 1 (1892), 79-292. | JFM

[S] G. Salmon, Lessons Introductory to the Higher Modern Algebra, Hodges, Figgis, and Co., 1885.

[Sch] G. Schwarz, On classical invariant theory and binary cubics, Ann. Inst. Fourier, 37-3 (1987), 191-216. | Zbl | MR | Numdam

[Sp] T.A. Springer, Invariant Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1977. | Zbl | MR

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