Regular Representation of Affine Kac-Moody Algebras
The question about commutative properties of the singularly perturbed self-adjoint operators arises in connection with the development of the quantum field theory. It is often necessary to know when a pair of unbounded closed self-adjoint commutative operators commute also if one of them or both were replaced by singularly perturbed operators i.e. by operators coinciding with the given operators on a dense subspace. The necessary and sufficient conditions under which the singularly perturbed self-adjoint operators commute are investigated in this note. This research may be applied to the theory of the singularly perturbed normal operators.
KeywordsCentral Charge Regular Representation Loop Group Cartan Matrix Moody Algebra
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