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The decompositions of the Fock and Basic modules of the aane Lie algebra ^ sl N into irreducible submodules of the Yangian algebra Y (gl N) are constructed. Each of the irreducible submodules admits the unique up to normalization eigenbasis of the maximal commutative subalgebra of the Yangian. The elements of this eigenbasis are identiied with specializations of Macdonald symmetric functions where both parameters of these functions approach an N th primitive root of unity.

Symmetric functions and the Yangian decomposition of the Fock and basic modules of the affine Lie algebra $\hat{\mathfrak{s}\mathfrak{l}}_{N}$