g-ENDOMORPHISM ALGEBRAS, AND DYNKIN POLYNOMIALS
نویسنده
چکیده
Recently, A.A. Kirillov introduced an interesting class of associative algebras connected with the adjoint representation of G [Ki]. In our paper, such algebras are called g-endomorphism algebras. Each g-endomorphism algebra is a module over the algebra of invariants k[g]; furthermore, it is a direct sum of modules of covariants. Hence it is a free graded finitely generated module over k[g]. The aim of this paper is to show that commutative g-endomorphism algebras have intriguing connections with representation theory, combinatorics, commutative algebra, and equivariant cohomology. Let πλ : G → GL(Vλ) be an irreducible representation, where λ stands for the highest weight of Vλ. Following Kirillov, one can form an associative k-algebra by taking the G-invariant elements in the G-module EndVλ ⊗ k[g]. That is, we set Cλ(g) = (EndVλ ⊗ k[g]) G .
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