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

Abstract

The decomposition of the Fock and basic modules of the affine Lie algebra $\mathfrak{sl}_{N}$ into irreducible submodules of the Yangian $Y(\mathfrak{gl}_N$ is 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 identified with specializations of Macdonald symmetric functions where both parameters of the latter approach an Nth primitive root of unity.