Several realizations of Fock modules for quantum toroidal algebras of sl(n)

Abstract

In this paper, we relate the well-known Fock representations of the quantum toroidal algebra of sl(n) to the vertex, shuffle, and L-operator representations of the same algebra. These identifications generalize those for the quantum toroidal algebra of gl(1), which were recently established by Feigin-Jimbo-Miwa-Mukhin.

v1: 24 pages. v2: Final version, 27 pages, references updated, several proofs expanded, a few mistakes corrected. To appear in Algebras and Representation Theory

References in corpus (2)

• The affine Yangian of ${\mathfrak{gl}}_1$ revisited
• Bethe subalgebras of quantum affine gl(n) via shuffle algebras

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