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

Bart De Bruyn UGent and M Kwiatkowski (2015) COMMUNICATIONS IN ALGEBRA. 43(12). p.5372-5398
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).
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Trivector, (Quasi-)Sp(V_f)-equivalence, Symplectic group, Spin module, Exterior power, Weyl module, HYPERPLANES, TRIVECTORS, GEOMETRIES, EMBEDDINGS, SPACES, DW(5
journal title
COMMUNICATIONS IN ALGEBRA
Commun. Algebr.
volume
43
issue
12
pages
5372 - 5398
Web of Science type
Article
Web of Science id
000361540800025
JCR category
MATHEMATICS
JCR impact factor
0.368 (2015)
JCR rank
263/312 (2015)
JCR quartile
4 (2015)
ISSN
0092-7872
DOI
10.1080/00927872.2014.975343
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
7140148
handle
http://hdl.handle.net/1854/LU-7140148
date created
2016-03-09 13:23:57
date last changed
2017-05-04 14:02:55
@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},
}

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.