$SL_2$, the cubic and the quartic

Papageorgiou, Yannis Y.

doi:10.5802/aif.1610

S L_{2}

, the cubic and the quartic

Papageorgiou, Yannis Y.

Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 29-71.

Résumé
Abstract

On donne une description de la restriction des modules de $S p_{4}$ à $S L_{2}$ , où $S L_{2}$ 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 $S p_{4}$ to $S L_{2}$ , 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.

MR Zbl

DOI : 10.5802/aif.1610

@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},
     mrnumber = {99f:20071},
     zbl = {0901.20030},
     language = {en},
     url = {http://www.numdam.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  - http://www.numdam.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 http://www.numdam.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. http://www.numdam.org/articles/10.5802/aif.1610/

Bibliographie
Cité par

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

[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. | MR | Zbl

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

[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. | MR | Zbl

[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. | MR | Zbl

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

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

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

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

[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. | Numdam | MR | Zbl

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

Cité par Sources :