Invariant ideals of polynomial algebras with multiplicity free group action
Compositio Mathematica (1989)
- Volume: 71, Issue: 2, page 181-227
- ISSN: 0010-437X
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topRuitenburg, G. C. M.. "Invariant ideals of polynomial algebras with multiplicity free group action." Compositio Mathematica 71.2 (1989): 181-227. <http://eudml.org/doc/89972>.
@article{Ruitenburg1989,
author = {Ruitenburg, G. C. M.},
journal = {Compositio Mathematica},
keywords = {algebraic group; irreducible linear representation; simply connected form; quotient map; G-action; induced action; G-orbits; graded G- invariant ideals; Young diagrams},
language = {eng},
number = {2},
pages = {181-227},
publisher = {Kluwer Academic Publishers},
title = {Invariant ideals of polynomial algebras with multiplicity free group action},
url = {http://eudml.org/doc/89972},
volume = {71},
year = {1989},
}
TY - JOUR
AU - Ruitenburg, G. C. M.
TI - Invariant ideals of polynomial algebras with multiplicity free group action
JO - Compositio Mathematica
PY - 1989
PB - Kluwer Academic Publishers
VL - 71
IS - 2
SP - 181
EP - 227
LA - eng
KW - algebraic group; irreducible linear representation; simply connected form; quotient map; G-action; induced action; G-orbits; graded G- invariant ideals; Young diagrams
UR - http://eudml.org/doc/89972
ER -
References
top- [Ab] S. Abeasis, Gli ideali GL(V)-invarianti in S(S2 V), Rendiconti Matematica (2), 13, serie IV (1980) 235-262. Zbl0512.14027
- [ADF] S. Abeasis and A. Del Fra, Young diagrams and ideas of pfaffians, Adv. in Math.35 (1980) 158-178. Zbl0444.20037MR560133
- [AM] M.F. Atiyah and I.G. Macdonald, Introduction to commutative algebra, Addison Wesley (1969). Zbl0175.03601MR242802
- [Br] M. Brion, Representations exceptionnelles des groupes semi-simples, Ann. scient. Ec. Norm. Sup.4e série, t.18 (1985) 345-387. Zbl0588.22010MR816368
- [CP] C de Concini and C. Procesi, Complete symmetric varieties, Lect. Notes in Math. 996, Springer Verlag (1983). Zbl0581.14041MR718125
- [CEP] C. de Concini, D. Eisenbud and C. Procesi, Young diagrams and determinantal varieties, Inventiones Math.56 (1980) 129-165. Zbl0435.14015MR558865
- [D] L. Dickson, A class of groups in an arbitrary realm connected with the configuration of the 27 lines on a cubic surface, Quarterly J. Pure and Appl. Math.33 (1901) 145-173. Zbl32.0133.01JFM32.0133.01
- [EH] D. Eisenbud and M. Hochster, A Nullstellensatz with nilpotents, and Zariski's main lemma on holomorphic functionsJournal of Algebra58 (17) 157-161. Zbl0417.14001MR535850
- [F] H. Freudenthal, Beziehungen der E7 und E8 zur Oktavenebene VIII, Proc. Kon. Ak. v. Wet. A62 (1959) 447-465. Zbl0128.15302
- [HO] G.J. Heckman and E.M. Opdam, Root systems and hypergeometric functions I, Comp. Math.64, (3) (1987) 329-352. Zbl0656.17006MR918416
- [H] G.J. Heckman, Root systems and hypergeometric functions II, Comp. Math.64, (3) (1987) 353-373. Zbl0656.17007MR918417
- [Hel1] S. Helgason, Differential geometry, Lie groups and symmetric spaces, Acad. Press. (1978). Zbl0451.53038MR514561
- [He12] S. Helgason, Groups and geometric analysis, Acad. Press. (1984). Zbl0543.58001MR754767
- [He13] S. Helgason, A duality for symmetric spaces with applications to group representations, Adv. in Math.5 (1970) 1-154. Zbl0209.25403MR263988
- [Hu1] J.E. Humphreys, Introduction to Lie algebras and representation theory, Springer Verlag (1972). Zbl0254.17004MR323842
- [Hu2] J.E. Humphreys, Linear algebraic groups, Springer Verlag (1975). Zbl0325.20039MR396773
- [Ka] V.G. Kac, Some remarks on nilpotent orbits, Journal of Algebra64 (1980) 190-213. Zbl0431.17007MR575790
- [Kr] H. Kraft, Geometrische Methoden in der Invariantentheorie, Friedr. Vieweg & Sohn (1984). Zbl0569.14003MR768181
- [LV] R. Lazarsfeld and A. Van de Ven, Topics in the geometry of projective space, Recent Work of F.L. Zak, Birkhäuser (1984). Zbl0564.14007MR808175
- [M] I.G. Macdonald, Symmetric functions and Hall polynomials, Clarendon Press., Oxford (1979). Zbl0487.20007MR553598
- [R] R.W. Richardson, Orbits, Invariants, and Representations Associated to Involutions of Reductive Groups, Inventiones Math.66 (1982) 287-312. Zbl0508.20021MR656625
- [V1] T. Vust, Opération de groupes réductifs dans un type de cônes presque homogènes, Bull. Soc. math. France102 (1974) 317-333. Zbl0332.22018MR366941
- [V2] T. Vust, Sur la théorie des invariants des groupes classiques, Ann. Inst. Fourier, Grenoble26 (1) (1976) 1-31. Zbl0314.20035MR404280
- [ZS] O. Zariski and P. Samuel, Commutative algebra, Vol. II, D. van Nostrand Company (1960). Zbl0121.27801MR120249
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