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

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.

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.

@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'institut Fourier},
     volume = {48},
     number = {1},
     year = {1998},
     doi = {10.5802/aif.1610},
     zbl = {0901.20030},
     mrnumber = {99f:20071},
     language = {en},
     url = {www.numdam.org/item/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. http://www.numdam.org/item/AIF_1998__48_1_29_0/

[Br] M. Brion, Représentations exceptionnelles des groupes semi-simples, Ann. Scient. Éc. Norm. Sup., 4e série, 18 (1985), 345-387. | Numdam | MR 87e:14043 | Zbl 0588.22010

[G] P. Gordan, Die simultanen Systeme binärer Formen, Math. Ann., 2 (1870), 227-280. | JFM 02.0059.01

[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 02.0065.02

[H-Per] R. Howe, Perspectives on invariant theory: Schur duality, multiplicity-free actions, and beyond, Isr. Math. Conf. Proc., 8 (1995), 1-182. | MR 96e:13006 | Zbl 0844.20027

[H-Rem] R. Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc., 313 (1989), 539-570. | MR 90h:22015a | Zbl 0674.15021

[HU] R. Howe and T. Umeda, The Capelli identity, the double commutant theorem and multiplicity-free actions, Math. Ann., 290 (1991), 565-619. | Zbl 0733.20019

[Hum] J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1972. | MR 48 #2197 | Zbl 0254.17004

[KKLV] F. Knop et Al., Algebraic Transformation Groups and Invariant Theory (H. Kraft et al., eds), Birkhäuser Basel Boston Berlin, 1989, 63-76. | Zbl 0682.00008

[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. | MR 88i:22035 | Zbl 0622.20033

[K] B. Kostant, A formula for the Multiplicity of a Weight, Trans. Amer. Math. Soc., 93 (1959), 53-73. | MR 22 #80 | Zbl 0131.27201

[LP1] P. Littelmann, A Generalization of the Littlewood-Richardson Rule, J. Alg., 130 (1990), 328-368. | MR 91f:22023 | Zbl 0704.20033

[LP2] P. Littelmann, A Littlewood-Richardson Rule for Symmetrizable Kac-Moody Algebras, Invent. Math., 116 (1994), 329-346. | MR 95f:17023 | Zbl 0805.17019

[LDE] D.E. Littlewood, On Invariants under Restricted Groups, Philos. Trans. Roy. Soc. A, 239 (1944), 387-417. | MR 7,6e | Zbl 0060.04403

[M] F. Meyer, Bericht über den gegenwärtigen Stand der Invariantentheorie, Jahresbericht der DMV, Band 1 (1892), 79-292. | JFM 24.0045.01

[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. | Numdam | MR 89h:14036 | Zbl 0597.14011

[Sp] T.A. Springer, Invariant Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1977. | MR 56 #5740 | Zbl 0346.20020