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A 14-dimensional module for the symplectic group: orbits on vectors

(2015) COMMUNICATIONS IN ALGEBRA. 43(12). p.5372-5398
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Abstract
Let F be a field, V a 6-dimensional F-vector space and f a nondegenerate alternating bilinear form on V. We consider a 14-dimensional module for the symplectic group Sp(V, f) congruent to Sp(6, F) associated with (V, f), and classify the orbits on vectors. For characteristic distinct from 2, this module is irreducible and isomorphic to the Weyl module of Sp(V, f) for the fundamental weight lambda(3). If the characteristic is 2, then the module is reducible as it contains an 8-dimensional submodule isomorphic to the spin module of Sp(V, f).
Keywords
Trivector, (Quasi-)Sp(V_f)-equivalence, Symplectic group, Spin module, Exterior power, Weyl module, HYPERPLANES, TRIVECTORS, GEOMETRIES, EMBEDDINGS, SPACES, DW(5

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Please use this url to cite or link to this publication:

Chicago
De Bruyn, Bart, and M Kwiatkowski. 2015. “A 14-dimensional Module for the Symplectic Group: Orbits on Vectors.” Communications in Algebra 43 (12): 5372–5398.
APA
De Bruyn, B., & Kwiatkowski, M. (2015). A 14-dimensional module for the symplectic group: orbits on vectors. COMMUNICATIONS IN ALGEBRA, 43(12), 5372–5398.
Vancouver
1.
De Bruyn B, Kwiatkowski M. A 14-dimensional module for the symplectic group: orbits on vectors. COMMUNICATIONS IN ALGEBRA. 2015;43(12):5372–98.
MLA
De Bruyn, Bart, and M Kwiatkowski. “A 14-dimensional Module for the Symplectic Group: Orbits on Vectors.” COMMUNICATIONS IN ALGEBRA 43.12 (2015): 5372–5398. Print.
@article{7140148,
  abstract     = {Let F be a field, V a 6-dimensional F-vector space and f a nondegenerate alternating bilinear form on V. We consider a 14-dimensional module for the symplectic group Sp(V, f) congruent to Sp(6, F) associated with (V, f), and classify the orbits on vectors. For characteristic distinct from 2, this module is irreducible and isomorphic to the Weyl module of Sp(V, f) for the fundamental weight lambda(3). If the characteristic is 2, then the module is reducible as it contains an 8-dimensional submodule isomorphic to the spin module of Sp(V, f).},
  author       = {De Bruyn, Bart and Kwiatkowski, M},
  issn         = {0092-7872},
  journal      = {COMMUNICATIONS IN ALGEBRA},
  keyword      = {Trivector,(Quasi-)Sp(V\_f)-equivalence,Symplectic group,Spin module,Exterior power,Weyl module,HYPERPLANES,TRIVECTORS,GEOMETRIES,EMBEDDINGS,SPACES,DW(5},
  language     = {eng},
  number       = {12},
  pages        = {5372--5398},
  title        = {A 14-dimensional module for the symplectic group: orbits on vectors},
  url          = {http://dx.doi.org/10.1080/00927872.2014.975343},
  volume       = {43},
  year         = {2015},
}

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