Symmetric functions and the Yangian decomposition of the Fock and Basic modules of the affine Lie algebra \hat{sl(N)}

Details Symmetric functions and the Yangian decomposition of the Fock and Basic modules of the affine Lie algebra \hat{sl(N)} Symmetric functions and the Yangian decomposition of the Fock and Basic modules of the affine Lie algebra \hat{sl(N)}

1997-05-14

arxiv.org/abs/q-alg/9705010v1

Mathematics

Quantum Algebra

45 pages, Latex2e

Scientific paper

The decompositions of the Fock and Basic modules of the affine Lie algebra \hat{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 identified with specializations of Macdonald symmetric functions where both parameters of these functions approach an N-th primitive root of unity.

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