Several realizations of Fock modules for toroidal Üq,d(sln)

Tsymbaliuk, Alexander

doi:10.1007/s10468-017-9761-5

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Several realizations of Fock modules for toroidal Ü_q,d(sl_n)

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Tsymbaliuk, Alexander
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s10468-017-9761-5
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Tsymbaliuk, A. (2019). Several realizations of Fock modules for toroidal Ü_q,d(sl_n). Algebras and Representation Theory, 22(1), 177-209. doi:10.1007/s10468-017-9761-5.

Cite as: https://hdl.handle.net/21.11116/0000-0004-755C-2

Abstract

In this paper, we relate the well-known
Fock representations of $\"U_{q,d}(\mathfrak{sl}_n)$ to the vertex, shuffle, and $L$-operator’ representations of $\"U_{q,d}(\mathfrak {sl}_n)$.
These identifications generalize those for the quantum toroidal algebra of $\mathfrak{gl}_1$, which were recently established in Feigin et al. (J. Phys. A 48(24), 244001, 2015).