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On the Grassmann modules for the unitary groups

Bart De Bruyn UGent (2010) LINEAR & MULTILINEAR ALGEBRA. 58(7). p.887-902
abstract
Let V be 2n-dimensional vector space over a field equipped with a nondegenerate skew--Hermitian form f of Witt index n epsilon 1, let 0 be the fix field of and let G denote the group of isometries of (V, f). For every k {1, ..., 2n}, there exist natural representations of the groups G U(2n, /0) and H = G SL(V) SU(2n, /0) on the k-th exterior power of V. With the aid of linear algebra, we prove some properties of these representations. We also discuss some applications to projective embeddings and hyperplanes of Hermitian dual polar spaces.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
hyperplane, DUAL POLAR SPACES, Hermitian dual polar space, Grassmann module, unitary group, EMBEDDINGS
journal title
LINEAR & MULTILINEAR ALGEBRA
Linear Multilinear Algebra
volume
58
issue
7
pages
887 - 902
Web of Science type
Article
Web of Science id
000281850900007
JCR category
MATHEMATICS
JCR impact factor
0.818 (2010)
JCR rank
72/276 (2010)
JCR quartile
2 (2010)
ISSN
0308-1087
DOI
10.1080/03081080903127270
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1108475
handle
http://hdl.handle.net/1854/LU-1108475
date created
2011-01-22 10:11:56
date last changed
2011-02-14 15:59:09
@article{1108475,
  abstract     = {Let V be 2n-dimensional vector space over a field equipped with a nondegenerate skew--Hermitian form f of Witt index n epsilon 1, let 0 be the fix field of and let G denote the group of isometries of (V, f). For every k \{1, ..., 2n\}, there exist natural representations of the groups G U(2n, /0) and H = G SL(V) SU(2n, /0) on the k-th exterior power of V. With the aid of linear algebra, we prove some properties of these representations. We also discuss some applications to projective embeddings and hyperplanes of Hermitian dual polar spaces.},
  author       = {De Bruyn, Bart},
  issn         = {0308-1087},
  journal      = {LINEAR \& MULTILINEAR ALGEBRA},
  keyword      = {hyperplane,DUAL POLAR SPACES,Hermitian dual polar space,Grassmann module,unitary group,EMBEDDINGS},
  language     = {eng},
  number       = {7},
  pages        = {887--902},
  title        = {On the Grassmann modules for the unitary groups},
  url          = {http://dx.doi.org/10.1080/03081080903127270},
  volume       = {58},
  year         = {2010},
}

Chicago
De Bruyn, Bart. 2010. “On the Grassmann Modules for the Unitary Groups.” Linear & Multilinear Algebra 58 (7): 887–902.
APA
De Bruyn, B. (2010). On the Grassmann modules for the unitary groups. LINEAR & MULTILINEAR ALGEBRA, 58(7), 887–902.
Vancouver
1.
De Bruyn B. On the Grassmann modules for the unitary groups. LINEAR & MULTILINEAR ALGEBRA. 2010;58(7):887–902.
MLA
De Bruyn, Bart. “On the Grassmann Modules for the Unitary Groups.” LINEAR & MULTILINEAR ALGEBRA 58.7 (2010): 887–902. Print.