Search and download archives of mathematical journals

  
 
  Table of contents for this issue | Previous article | Next article
Schwarz, Gerry W.; Wehlau, David L.
Invariants of four subspaces. Annales de l'institut Fourier, 48 no. 3 (1998), p. 667-697
Full text djvu | pdf | Reviews MR 99i:14055 | Zbl 0899.20024

stable URL: http://www.numdam.org/item?id=AIF_1998__48_3_667_0

Lookup this article on the publisher's site

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.

Bibliography

[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.  MR 52 #13876 |  Zbl 0279.08001
[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.  MR 44 #2762 |  Zbl 0294.15001
[HoHu] R. HOWE and R. HUANG, Projective invariants of four subspaces, Adv. in Math., 118 #2 (1996), 295-336.  MR 97b:13005 |  Zbl 0852.15021
[Huan] R. HUANG, Invariants of sets of linear varieties, Proc. Natl. Acad. Sci. USA, 87 #12 (1990), 4557-4560.  MR 91i:05126 |  Zbl 0717.15020
[Kac] V.G. KAC, Infinite root systems, representations of graphs and invariant theory, Inv. Math., 56 (1980), 57-92.  Zbl 0427.17001
[Kempf] G. KEMPF, Some quotient surfaces are smooth, Mich. Math. J., 27 (1980), 295-299.
Article |  MR 81m:14009 |  Zbl 0465.14018
[LuRi] D. LUNA and R.W. RICHARDSON, A generalization of the Chevalley restriction theorem, Duke Math. J., 46 (1979), 487-496.
Article |  MR 80k:14049 |  Zbl 0444.14010
[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.
Numdam |  Zbl 0276.14017
[Na] L.A. NAZAROVA, Representation of a tetrad, Izv. Akad. Nauk SSSR, Ser., 31 (1967), 1361-1378 = Math. USSR Izv., 1 (1967), 1305-1322.  MR 36 #6400 |  Zbl 0222.16028
[Po] V.L. POPOV, Stability criteria for actions of a semisimple group on a factorial manifold., Math. USSR Izv., 4 (1970), 527-535.  Zbl 0261.14011
[Ring] C.M. RINGEL, The rational invariants of the tame quivers, Invent. Math., 58 (1980), 217-239.  MR 81f:16048 |  Zbl 0433.15009
[Sch1] G.W. SCHWARZ, Lifting smooth homotopies of orbit spaces, Publ. Math. IHES, 51 (1980), 37-135.
Numdam |  MR 81h:57024 |  Zbl 0449.57009
[Sch2] G.W. SCHWARZ, Representations of simple Lie groups with a free module of covariants, Invent. Math., 50 (1978), 1-12.  MR 80c:14008 |  Zbl 0391.20033
[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.  Zbl 0722.14031
[Turn] H.W. TURNBULL, The projective invariants of four medials, Proc. Edinb. Math. Soc. II, Ser. 7 (1942), 55-72.  MR 4,110a |  Zbl 0063.07882
[Wehl] D. WEHLAU, Equidimensional Representations of 2-Simple groups, J. Algebra, 154 (2) (1993), 437-489.  MR 93k:14064 |  Zbl 0820.20051
Copyright Cellule MathDoc 2013 | Credit | Site Map