On the Grassmann modules for the symplectic groups

DOI10.1016/j.jalgebra.2010.03.033zbMath1204.15037OpenAlexW2058823627MaRDI QIDQ986065

Bart De Bruyn

Publication date: 11 August 2010

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1854/LU-1105421

zbMATH Keywords

symplectic groupdual polar spaceGrassmann embeddingminimal full polarized embeddingGrassmann module

Mathematics Subject Classification ID

Representations of finite groups of Lie type (20C33) Quadratic and bilinear forms, inner products (15A63) Exterior algebra, Grassmann algebras (15A75) Polar geometry, symplectic spaces, orthogonal spaces (51A50)

Related Items

Hesselink normal forms of unipotent elements in some representations of classical groups in characteristic two, Hyperplanes and projective embeddings of dual polar spaces, On the trivectors of a 6-dimensional symplectic vector space, On extensions of hyperplanes of dual polar spaces, The classification of the trivectors of a six-dimensional symplectic space: Summary, consequences and connections, On certain forms and quadrics related to symplectic dual polar spaces in characteristic 2, Monodromy of the \(\mathrm{SL}(n)\) and \(\mathrm{GL}(n)\) Hitchin fibrations, Invariant forms on irreducible modules of simple algebraic groups, On the Grassmann modules for the unitary groups

Cites Work

• Unnamed Item
• Analog of the space of primitive forms over a field of positive characteristic
• Minimal full polarized embeddings of dual polar spaces
• Some subspaces of the \(k\)th exterior power of a symplectic vector space
• Polarized and homogeneous embeddings of dual polar spaces
• The submodule lattice of Weyl modules for symplectic groups with fundamental highest weights
• Buildings of spherical type and finite BN-pairs
• The weyl modules and the irreducible representations of the symplectic group with the fundamental highest weights