S L 2 , the cubic and the quartic

Yannis Y. Papageorgiou

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 1, page 29-71
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Papageorgiou, Yannis Y.. "$SL_2$, the cubic and the quartic." Annales de l'institut Fourier 48.1 (1998): 29-71. <http://eudml.org/doc/75281>.

@article{Papageorgiou1998,
abstract = {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.},
author = {Papageorgiou, Yannis Y.},
journal = {Annales de l'institut Fourier},
keywords = {binary forms; algebras of covariants; branching rules; multiplicity formula; minimal systems of generators; geometric realizations},
language = {eng},
number = {1},
pages = {29-71},
publisher = {Association des Annales de l'Institut Fourier},
title = {$SL_2$, the cubic and the quartic},
url = {http://eudml.org/doc/75281},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Papageorgiou, Yannis Y.
TI - $SL_2$, the cubic and the quartic
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 1
SP - 29
EP - 71
AB - 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.
LA - eng
KW - binary forms; algebras of covariants; branching rules; multiplicity formula; minimal systems of generators; geometric realizations
UR - http://eudml.org/doc/75281
ER -

References

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  1. [Br] M. BRION, Représentations exceptionnelles des groupes semi-simples, Ann. Scient. Éc. Norm. Sup., 4e série, 18 (1985), 345-387. Zbl0588.22010MR87e:14043
  2. [G] P. GORDAN, Die simultanen Systeme binärer Formen, Math. Ann., 2 (1870), 227-280. Zbl02.0059.01JFM02.0059.01
  3. [GI] P. GORDAN, Vorlesungen über Invarianten Theorie, reprinted by Chelsea Publishing Co., New York, 1987. 
  4. [Gu] S. GUNDELFINGER, Zur Theorie des simultanen Systems einer cubischen und einer biquadratischen binären Form, J.B. Metzler, Stuttgart, 1869. Zbl02.0065.02JFM02.0065.02
  5. [H-Per] R. HOWE, Perspectives on invariant theory: Schur duality, multiplicity-free actions, and beyond, Isr. Math. Conf. Proc., 8 (1995), 1-182. Zbl0844.20027MR96e:13006
  6. [H-Rem] R. HOWE, Remarks on classical invariant theory, Trans. Amer. Math. Soc., 313 (1989), 539-570. Zbl0674.15021MR90h:22015a
  7. [HU] R. HOWE and T. UMEDA, The Capelli identity, the double commutant theorem and multiplicity-free actions, Math. Ann., 290 (1991), 565-619. Zbl0733.20019
  8. [Hum] J. HUMPHREYS, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1972. Zbl0254.17004MR48 #2197
  9. [KKLV] F. KNOP et AL., Algebraic Transformation Groups and Invariant Theory (H. Kraft et al., eds), Birkhäuser Basel Boston Berlin, 1989, 63-76. Zbl0682.00008
  10. [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. Zbl0622.20033MR88i:22035
  11. [K] B. KOSTANT, A formula for the Multiplicity of a Weight, Trans. Amer. Math. Soc., 93 (1959), 53-73. Zbl0131.27201MR22 #80
  12. [LP1] P. LITTELMANN, A Generalization of the Littlewood-Richardson Rule, J. Alg., 130 (1990), 328-368. Zbl0704.20033MR91f:22023
  13. [LP2] P. LITTELMANN, A Littlewood-Richardson Rule for Symmetrizable Kac-Moody Algebras, Invent. Math., 116 (1994), 329-346. Zbl0805.17019MR95f:17023
  14. [LDE] D.E. LITTLEWOOD, On Invariants under Restricted Groups, Philos. Trans. Roy. Soc. A, 239 (1944), 387-417. Zbl0060.04403MR7,6e
  15. [M] F. MEYER, Bericht über den gegenwärtigen Stand der Invariantentheorie, Jahresbericht der DMV, Band 1 (1892), 79-292. Zbl24.0045.01JFM24.0045.01
  16. [S] G. SALMON, Lessons Introductory to the Higher Modern Algebra, Hodges, Figgis, and Co., 1885. 
  17. [Sch] G. SCHWARZ, On classical invariant theory and binary cubics, Ann. Inst. Fourier, 37-3 (1987), 191-216. Zbl0597.14011MR89h:14036
  18. [Sp] T.A. SPRINGER, Invariant Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1977. Zbl0346.20020MR56 #5740

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