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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
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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.
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:

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 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},
}

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