Invariant theory of the block diagonal subgroups of GL(n,C) and generalized Casimir operators
1992; Elsevier BV; Volume: 145; Issue: 1 Linguagem: Inglês
10.1016/0021-8693(92)90184-n
ISSN1090-266X
Autores Tópico(s)Algebraic structures and combinatorial models
ResumoLet C be the field of complex numbers and let GL(n,C) denote the general linear group of order n over C. Let n be the sum of m positive integers p1, …, pm and consider the block diagonal subgroup GL(p1,C)x…xGL(pm,C). The adjoint representation of the Lie group GL(n,C) on its Lie algebra gives rise to the coadjoint representation of GL(n,C) on the symmetric algebra of all polynomial functions on GL(n,C). The polynomials that are fixed by the restriction of the coadjoint representation to the block diagonal subgroup form a subalgebra called the algebra of invariants. A finite set of generators of this algebra is explicitly determined and the connection with the generalized Casimir invariant differential operators is established.
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