First Fundamental Theorem of Invariant Theory for covariants of classical groups

2000/06/15 by D. A. Shmel'kin, D. A. Shmelkin, Shmel'kin, D. A.
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.AG #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0006110

13 pages, LaTeX 2.09

arxiv created 2000/06/15 · openalex publication_date 2000/06/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let U(G) be a maximal unipotent subgroup of one of classical groups G=GL(V),O(V),Sp(V). Let W be a direct sum of copies of V and its dual V*. For the natural action U(G):W, we describe a minimal system of homogeneous generators for the algebra of U(G)-invariant regular functions on W. For G=GL(V), we also describe the syzygies among these generators in some particular cases.

Related

• Polynomial Invariant Theory of the Classical Groups
• Classical invariant theory for free metabelian Lie algebras
• On the irreducibility of symmetrizations of cross-characteristic representations of finite classical groups
• Some complete intersection symplectic quotients in positive characteristic: invariants of a vector and a covector
• On Chevalley-Shephard-Todd's theorem in positive characteristic