### On the Grassmann modules for the unitary groups

(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:
http://hdl.handle.net/1854/LU-1108475

- author
- De Bruyn, Bart UGent
- organization
- year
- 2010
- 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
- 2016-12-19 15:41:08

@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.