# Quantum continuous $\mathfrak{gl}_{\infty}$: Semiinfinite construction of representations

@article{Feigin2011QuantumC,
title={Quantum continuous \$\mathfrak\{gl\}_\{\infty\}\$: Semiinfinite construction of representations},
author={B. Feigin and E. Feigin and M. Jimbo and T. Miwa and E. Mukhin},
journal={Journal of Mathematics of Kyoto University},
year={2011},
volume={51},
pages={337-364}
}
• B. Feigin, +2 authors E. Mukhin
• Published 2011
• Mathematics
• Journal of Mathematics of Kyoto University
We begin a study of the representation theory of quantum continuous $\mathfrak{gl}_\infty$, which we denote by $\mathcal E$. This algebra depends on two parameters and is a deformed version of the enveloping algebra of the Lie algebra of difference operators acting on the space of Laurent polynomials in one variable. Fundamental representations of $\mathcal E$ are labeled by a continuous parameter $u\in {\mathbb C}$. The representation theory of $\mathcal E$ has many properties familiar from… Expand
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