A note on the zeroth products of Frenkel-Jing operators

作者：Kozic Slaven^*

来源：Journal of Algebra and Its Applications, 2017, 16(3): 1750053.

DOI：10.1142/S0219498817500530

• Affine Lie algebra
• quantum affine algebra
• quantum vertex algebra
• highest weight module

Let (g) over cap be an untwisted affine Kac-Moody Lie algebra. The top of every irreducible highest weight integrable bg-module is the finite-dimensional irreducible (g) over cap -module, where the action of the simple Lie algebra g is given by zeroth products arising from the underlying vertex operator algebra theory. Motivated by this fact, we consider zeroth products of level 1 Frenkel-Jing operators corresponding to Drinfeld realization of the quantum affine algebra U-q((Sl) over capn+ 1). By applying these products, which originate from the quantum vertex algebra theory developed by Li, on the extension of Koyama vertex operator Y-i(z), we obtain an infinite-dimensional vector space < Y-i(z)>. Next, we introduce an associative algebra U-q(sl(n)+ 1)(z), a certain quantum analogue of the universal enveloping algebra U(sl(n)+ 1), and construct some infinite-dimensional U-q(sl(n)+ 1)(z)-modules L(lambda(i))(z) corresponding to the finite-dimensional irreducible U-q(sl(n)+ 1)-modules L(lambda(i)). We show that the space < Yi(z)> carries a structure of an U-q(sl(n)+ 1)(z)-module and, furthermore, we prove that the U-q(sl(n)+ 1)(z)-module < Yi(z)> is isomorphic to the U-q(sl(n)+ 1)(z)-module L(lambda(i))(z).

• 出版日期2017-3