Invariants of four subspaces

Gerry W. Schwarz; David L. Wehlau

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 3, page 667-697
  • ISSN: 0373-0956

Abstract

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We consider problems in invariant theory related to the classification of four vector subspaces of an n -dimensional complex vector space. We use castling techniques to quickly recover results of Howe and Huang on invariants. We further obtain information about principal isotropy groups, equidimensionality and the modules of covariants.

How to cite

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Schwarz, Gerry W., and Wehlau, David L.. "Invariants of four subspaces." Annales de l'institut Fourier 48.3 (1998): 667-697. <http://eudml.org/doc/75298>.

@article{Schwarz1998,
abstract = {We consider problems in invariant theory related to the classification of four vector subspaces of an $n$-dimensional complex vector space. We use castling techniques to quickly recover results of Howe and Huang on invariants. We further obtain information about principal isotropy groups, equidimensionality and the modules of covariants.},
author = {Schwarz, Gerry W., Wehlau, David L.},
journal = {Annales de l'institut Fourier},
keywords = {invariants; equidimensionality; castling; complex vector spaces; isotropy groups; modules of covariants},
language = {eng},
number = {3},
pages = {667-697},
publisher = {Association des Annales de l'Institut Fourier},
title = {Invariants of four subspaces},
url = {http://eudml.org/doc/75298},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Schwarz, Gerry W.
AU - Wehlau, David L.
TI - Invariants of four subspaces
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 3
SP - 667
EP - 697
AB - We consider problems in invariant theory related to the classification of four vector subspaces of an $n$-dimensional complex vector space. We use castling techniques to quickly recover results of Howe and Huang on invariants. We further obtain information about principal isotropy groups, equidimensionality and the modules of covariants.
LA - eng
KW - invariants; equidimensionality; castling; complex vector spaces; isotropy groups; modules of covariants
UR - http://eudml.org/doc/75298
ER -

References

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  1. [BGP] I.N. BERNSTEIN, I.M. GEL'FAND and V.A. PONOMAREV, Coxeter functions and Gabriel's theorem, Russian Math. Surveys, 28 (1973), 17-32. Zbl0279.08001MR52 #13876
  2. [GP] I.M. GEL'FAND and V.A. PONOMAREV, Quadruples of subspaces of a finite-dimensional vector space, Dokl. Akad. Nauk SSSR, 197 (1971), 762-765 = Soviet Math. Doklady, 12 (1971), 535-539. Zbl0294.15001MR44 #2762
  3. [HoHu] R. HOWE and R. HUANG, Projective invariants of four subspaces, Adv. in Math., 118 #2 (1996), 295-336. Zbl0852.15021MR97b:13005
  4. [Huan] R. HUANG, Invariants of sets of linear varieties, Proc. Natl. Acad. Sci. USA, 87 #12 (1990), 4557-4560. Zbl0717.15020MR91i:05126
  5. [Kac] V.G. KAC, Infinite root systems, representations of graphs and invariant theory, Inv. Math., 56 (1980), 57-92. Zbl0427.17001
  6. [Kempf] G. KEMPF, Some quotient surfaces are smooth, Mich. Math. J., 27 (1980), 295-299. Zbl0465.14018MR81m:14009
  7. [LuRi] D. LUNA and R.W. RICHARDSON, A generalization of the Chevalley restriction theorem, Duke Math. J., 46 (1979), 487-496. Zbl0444.14010MR80k:14049
  8. [LuVu] D. LUNA and Th. VUST, Un théorème sur les orbites affines des groupes algébriques semi-simples, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 27 (1973), 527-535. Zbl0276.14017
  9. [Na] L.A. NAZAROVA, Representation of a tetrad, Izv. Akad. Nauk SSSR, Ser., 31 (1967), 1361-1378 = Math. USSR Izv., 1 (1967), 1305-1322. Zbl0222.16028MR36 #6400
  10. [Po] V.L. POPOV, Stability criteria for actions of a semisimple group on a factorial manifold., Math. USSR Izv., 4 (1970), 527-535. Zbl0261.14011
  11. [Ring] C.M. RINGEL, The rational invariants of the tame quivers, Invent. Math., 58 (1980), 217-239. Zbl0433.15009MR81f:16048
  12. [Sch1] G.W. SCHWARZ, Lifting smooth homotopies of orbit spaces, Publ. Math. IHES, 51 (1980), 37-135. Zbl0449.57009MR81h:57024
  13. [Sch2] G.W. SCHWARZ, Representations of simple Lie groups with a free module of covariants, Invent. Math., 50 (1978), 1-12. Zbl0391.20033MR80c:14008
  14. [Slod] P. SLODOWY, Der Scheibensatz für algebraische Transformationsgruppen, in Algebraic Transformation Groups and Invariant Theory, DMV Seminar, 13 (1989), Birkhäuser Verlag, Basel-Boston, 89-113. Zbl0722.14031
  15. [Turn] H.W. TURNBULL, The projective invariants of four medials, Proc. Edinb. Math. Soc. II, Ser. 7 (1942), 55-72. Zbl0063.07882MR4,110a
  16. [Wehl] D. WEHLAU, Equidimensional Representations of 2-Simple groups, J. Algebra, 154 (2) (1993), 437-489. Zbl0820.20051MR93k:14064

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