105
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A 14-dimensional Module for the Symplectic Group: Orbits on Vectors

&
Pages 5372-5398 | Received 10 Sep 2013, Published online: 24 Aug 2015

REFERENCES

  • Aschbacher , M. ( 1987 ). The 27-dimensional module for E 6. I . Invent. Math. 89 : 159 – 195 .
  • Capdevielle , B. ( 1972 ). Classification des formes trilinéaires alternées en dimension 6 . Enseignement Math. 18 : 225 – 243 .
  • Cohen , A. M. , Cooperstein , B. N. ( 1988 ). The 2-spaces of the standard E 6(q)-module. Geometries and groups (Noordwijkerhout, 1986) . Geom. Dedicata 25 : 467 – 480 .
  • Cohen , A. M. , Helminck , A. G. ( 1988 ). Trilinear alternating forms on a vector space of dimension 7 . Comm. Algebra 16 : 1 – 25 .
  • Cohen , A. M. , Wales , D. B. ( 1996 ). GL(4)-orbits in a 16-dimensional module for characteristic 3 . J. Algebra 185 : 85 – 107 .
  • Cohn , P. M. ( 2003 ). Further Algebra and Applications . London : Springer-Verlag London .
  • Cooperstein , B. N. ( 1995 ). The fifty-six-dimensional module for E 7. I. A four form for E 7 . J. Algebra 173 : 361 – 389 .
  • Cooperstein , B. N. ( 1998 ). On the generation of dual polar spaces of symplectic type over finite fields . J. Combin. Theory Ser. A 83 : 221 – 232 .
  • Cooperstein , B. N. , De Bruyn , B. ( 2009 ). Points and hyperplanes of the universal embedding space of the dual polar space DW(5, q), q odd . Michigan Math. J. 58 : 195 – 212 .
  • De Bruyn , B. ( 2009 ). Hyperplanes of DW(5, 𝕂) with 𝕂 a perfect field of characteristic 2 . J. Algebraic Combin. 30 : 567 – 584 .
  • De Bruyn , B. ( 2009 ). Some subspaces of the k-th exterior power of a symplectic vector space . Linear Algebra Appl. 430 : 3095 – 3104 .
  • De Bruyn , B. ( 2011 ). On polyvectors of vector spaces and hyperplanes of projective Grassmannians . Linear Algebra Appl. 435 : 1055 – 1084 .
  • De Bruyn , B. , Kwiatkowski , M. ( 2011 ). On the trivectors of a 6-dimensional symplectic vector space . Linear Algebra Appl. 435 : 289 – 306 .
  • De Bruyn , B. , Kwiatkowski , M. ( 2012 ). On the trivectors of a 6-dimensional symplectic vector space. II . Linear Algebra Appl. 437 : 1215 – 1233 .
  • De Bruyn , B. , Kwiatkowski , M. ( 2013 ). On the trivectors of a 6-dimensional symplectic vector space. III . Linear Algebra Appl. 438 : 374 – 398 .
  • De Bruyn , B. , Kwiatkowski , M. ( 2013 ). On the trivectors of a 6-dimensional symplectic vector space. IV . Linear Algebra Appl. 438 : 2405 – 2429 .
  • De Bruyn , B. , Kwiatkowski , M. (2013). On trivectors and hyperplanes of symplectic dual polar spaces: The deep quads, Preprint.
  • Djoković , D. Ž. ( 1983 ). Classification of trivectors of an eight-dimensional real vector space . Linear and Multilinear Algebra 13 : 3 – 39 .
  • Gow , R. ( 1997 ). Contraction of exterior powers in characteristic 2 and the spin module . Geom. Dedicata 64 : 283 – 295 .
  • Guralnick , R. M. , Liebeck , M. W. , Macpherson , D. , Seitz , G. M. ( 1997 ). Modules for algebraic groups with finitely many orbits on subspaces . J. Algebra 196 : 211 – 250 .
  • Gurevich , G. B. ( 1933 ). Sur les formes canoniques d'un trivecteur dans l'espace à six dimensions . C. R. Acad. Sci. (Paris) 197 : 384 .
  • Gurevich , G. B. ( 1935 ). L'algèbre du trivecteur. Trudy Sem. Vektor. Tenzor. Anal. No. II-III:51–118 .
  • Gurevich , G. B. ( 1935 ). Classification des trivecteurs ayant le rang huit . Dokl. Akad. Nauk SSSR II ( 5–6 ): 355 – 356 .
  • Igusa , J.-I. ( 1970 ). A classification of spinors up to dimension twelve . Amer. J. Math. 92 : 997 – 1028 .
  • Kasikova , A. , Shult , E. ( 2001 ). Absolute embeddings of point-line geometries . J. Algebra 238 : 265 – 291 .
  • Popov , V. L. ( 1980 ). Classification of spinors of dimension fourteen . Trans. Mosc. Math. Soc. 1 : 181 – 232 .
  • Premet , A. A. , Suprunenko , I. D. ( 1983 ). The Weyl modules and the irreducible representations of the symplectic group with the fundamental highest weights . Comm. Algebra 11 : 1309 – 1342 .
  • Reichel , W. ( 1907 ). Über die trilinearen alternierenden Formen in 6 und 7 Veränderlichen. Dissertation, Greifswald .
  • Revoy , Ph. ( 1979 ). Trivecteurs de rang 6. Colloque sur les Formes Quadratiques (Montpellier, 1977) . Bull. Soc. Math. France Mém. 59 : 141 – 155 .
  • Revoy , Ph. ( 1988 ). Formes trilinéaires alternées de rang 7 . Bull. Sci. Math. 112 : 357 – 368 .
  • Ronan , M. A. ( 1987 ). Embeddings and hyperplanes of discrete geometries . European J. Combin. 8 : 179 – 185 .
  • Schouten , J. A. ( 1931 ). Klassifizierung der alternierenden Grössen dritten Grades in 7 Dimensionen . Rend. Circ. Mat. Palermo 55 : 137 – 156 .
  • Vinberg , È. B. , Èlašvili , A. G. ( 1978 ). Classification of trivectors of a nine-dimensional space . Trudy Sem. Vektor. Tenzor. Anal. 18 : 197 – 233 .
  • Westwick , R. ( 1981 ). Real trivectors of rank seven . Linear and Multilinear Algebra 10 : 183 – 204 .
  • Communicated by P. Tiep.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.