On the Grassmann modules for the unitary groups
 Author
 Bart De Bruyn (UGent)
 Organization
 Abstract
 Let V be 2ndimensional vector space over a field equipped with a nondegenerate skewHermitian 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 kth 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.
 Keywords
 hyperplane, DUAL POLAR SPACES, Hermitian dual polar space, Grassmann module, unitary group, EMBEDDINGS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU1108475
 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.
@article{1108475, abstract = {Let V be 2ndimensional vector space over a field equipped with a nondegenerate skewHermitian 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 kth 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 = {03081087}, journal = {LINEAR \& MULTILINEAR ALGEBRA}, keyword = {hyperplane,DUAL POLAR SPACES,Hermitian dual polar space,Grassmann module,unitary group,EMBEDDINGS}, language = {eng}, number = {7}, pages = {887902}, title = {On the Grassmann modules for the unitary groups}, url = {http://dx.doi.org/10.1080/03081080903127270}, volume = {58}, year = {2010}, }
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