1998/04/27 by Alexander Molev · 1 citation
Mathematics · #Adjoint representation of a Lie algebra #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Basis (linear algebra) #Geometry #Lie algebra #Lie conformal algebra #Mathematics #Moment map #Pure mathematics #Representation of a Lie group #Symplectic geometry #Symplectic group #Symplectic representation #math.QA #math.RT #msc:17B10 #msc:81R10
paper · pdf · doi:10.1007/s002200050570
published as Comm. Math. Phys. 201 (1999), 591--618. · 34 pages, AmSTeX
arxiv created 1998/04/27 · openalex publication_date 1999/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A basis for each finite-dimensional irreducible representation of the symplectic Lie algebra sp(2n) is constructed. The basis vectors are expressed in terms of the Mickelsson lowering operators. Explicit formulas for the matrix elements of generators of sp(2n) in this basis are given. The basis is natural from the viewpoint of the representation theory of the Yangians. The key role in the construction is played by the fact that the subspace of sp(2n-2)-highest vectors in any finite-dimensional irreducible representation of sp(2n) admits a natural structure of a representation of the Yangian Y(gl(2)).