A 14-dimensional Module for the Symplectic Group: Orbits on Vectors

DOI10.1080/00927872.2014.975343zbMath1334.15065OpenAlexW2258633386MaRDI QIDQ3448583

Mariusz Kwiatkowski, Bart De Bruyn

Publication date: 26 October 2015

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

Full work available at URL: https://biblio.ugent.be/publication/7140148

zbMATH Keywords

symplectic groupWeyl moduleexterior powerspin moduletrivectornondegenerate alternating bilinear form(quasi-)\(\mathrm{Sp}(V,f)\)-equivalence

Mathematics Subject Classification ID

Quadratic and bilinear forms, inner products (15A63) Exterior algebra, Grassmann algebras (15A75) Other special types of modules and ideals in commutative rings (13C13)

Cites Work

• On the trivectors of a 6-dimensional symplectic vector space. II
• On polyvectors of vector spaces and hyperplanes of projective Grassmannians
• Embeddings and hyperplanes of discrete geometries
• Contraction of exterior powers in characteristic \(2\) and the spin module
• Hyperplanes of \(DW(5,{\mathbb{K}})\) with \({\mathbb{K}}\) a perfect field of characteristic 2
• Some subspaces of the \(k\)th exterior power of a symplectic vector space
• Points and hyperplanes of the universal embedding space of the dual polar space DW\((5,q)\), \(q\) odd
• The 27-dimensional module for \(E_ 6\). I
• On the generation of dual polar spaces of symplectic type over finite fields
• Modules for algebraic groups with finitely many orbits on subspaces
• \(\text{GL}(4)\)-orbits in a \(16\)-dimensional module for characteristic \(3\)
• The fifty-six-dimensional module for \(E_ 7\). I: A four form for \(E_ 7\)
• On the trivectors of a 6-dimensional symplectic vector space. III
• On the trivectors of a 6-dimensional symplectic vector space. IV
• On the trivectors of a 6-dimensional symplectic vector space
• Classification of trivectors of an eight-dimensional real vector space
• The weyl modules and the irreducible representations of the symplectic group with the fundamental highest weights
• Trilinear alternating forms on a vector space of dimension 7
• Real trivectors of rank seven
• Klassifizierung der alternierenden Gröszen dritten Grades in 7 Dimensionen
• A Classification of Spinors Up to Dimension Twelve
• Absolute embeddings of point-line geometries

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