quantum vertex
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2020 ◽  
Vol 61 (1) ◽  
pp. 011701
Author(s):  
Alberto De Sole ◽  
Matteo Gardini ◽  
Victor G. Kac

2019 ◽  
Vol 109 (11) ◽  
pp. 2439-2471 ◽  
Author(s):  
Marijana Butorac ◽  
Naihuan Jing ◽  
Slaven Kožić

2018 ◽  
Vol 511 ◽  
pp. 182-214
Author(s):  
Haisheng Li ◽  
Shaobin Tan ◽  
Qing Wang

2017 ◽  
Vol 8 (1) ◽  
Author(s):  
C. Chamon ◽  
E. R. Mucciolo ◽  
A. E. Ruckenstein ◽  
Z.-C. Yang

2017 ◽  
Vol 16 (03) ◽  
pp. 1750053 ◽  
Author(s):  
Slaven Kožić

Let [Formula: see text] be an untwisted affine Kac–Moody Lie algebra. The top of every irreducible highest weight integrable [Formula: see text]-module is the finite-dimensional irreducible [Formula: see text]-module, where the action of the simple Lie algebra [Formula: see text] is given by zeroth products arising from the underlying vertex operator algebra theory. Motivated by this fact, we consider zeroth products of level [Formula: see text] Frenkel–Jing operators corresponding to Drinfeld realization of the quantum affine algebra [Formula: see text]. By applying these products, which originate from the quantum vertex algebra theory developed by Li, on the extension of Koyama vertex operator [Formula: see text], we obtain an infinite-dimensional vector space [Formula: see text]. Next, we introduce an associative algebra [Formula: see text], a certain quantum analogue of the universal enveloping algebra [Formula: see text], and construct some infinite-dimensional [Formula: see text]-modules [Formula: see text] corresponding to the finite-dimensional irreducible [Formula: see text]-modules [Formula: see text]. We show that the space [Formula: see text] carries a structure of an [Formula: see text]-module and, furthermore, we prove that the [Formula: see text]-module [Formula: see text] is isomorphic to the [Formula: see text]-module [Formula: see text].


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