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

1997/05/14 by Denis Uglov, Uglov, Denis
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9705010

45 pages, Latex2e

arxiv created 1997/05/14 · openalex publication_date 1997/05/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• Yangian actions on higher level irreducible integrable modules of affine gl(N)
• Orthogonalization and polarization of Yangians
• Representation Theory of the Twisted Yangians in Complex Rank
• Yangians and Classical Lie Algebras, Part II. Sklyanin determinant, Laplace operators and characteristic identities
• Modules for Relative Yangians (Family Algebras) and Kazhdan-Lusztig Polynomials