The Decomposition Problem Of A Highest Weight Irreducible ?-Module As G-Module

Let g be the finite dimensional simple Lie algebra over the complex number field.The untwisted affine Lie algebra?can be realized as a 1-dimensional central extension of the loop algebra of g.Asgcan be regarded as a Lie subalgebra of ? in the natural way,any?-module is ag-module.The irreducible decomposition problem of a highest weight irreducible?-module asg-module is still unsolved.In addition,The highest weight representation of affine Lie algebras is closely related to the partition theory.In this paper,we mainly study a special case of the above problem:how to describe the irreducible decomposition of a highest weight?-moduleL?7??43?₀?8?asg-module wheng?28?sl₂.For this purpose,we first prove an identity of partitions,and then give the complete description of the irreducible decomposition problem by the result of the identity.