Charles W. Curtis

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The representation theory of a group G over the field of complex numbers involves two problems: first, the construction of the irreducible representations of G; and second, the problem of expressing each suitably restricted complex valued function on G, as a linear combination (or a limit of linear combinations), of the coefficients of the irreducible(More)
Let £ be a split semisimple Lie algebra over a field <E> of characteristic zero and <£ = 3C+ ]C«eA«£a be the rootspace decomposition of <£ relative to a splitting Cartan subalgebra 5C, where the subset A of 3C* is the corresponding root-system. Fix a simple system of roots {c*i, «2, • • • , ai}, for which the positive (resp. negative) roots are denoted by(More)
Introduction. In this paper it is proved that the irreducible projective representations of the group G of automorphisms of a Lie algebra of classical type constructed in [2] remain irreducible and inequivalent when restricted to the subgroup Go of G generated by the oneparameter subgroups {exp(ad£ea)} where a ranges over the set of roots of ? with respect(More)
1. Introduction. We shall say that an integral domain1 R satisfies condition (M) if any two nonzero elements of R have a nonzero common right multiple. In this note it is proved that if 5 is an extension of a ring R such that S is, roughly speaking, a noncommutative polynomial ring in one variable with R as a coefficient ring, and if R has the property (M),(More)
This paper is about some graph isomorphisms between the Auslander-Reiten quivers of the path algebras of quivers with underlying Dynkin diagrams of type Al, and the weight diagrams or the weight graphs relative to some basic (adjoint) representations of a semi-simple complex Lie algebra associated to the same Dynkin diagrams. The crucial point is that, in(More)