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Simple weight modules for Yangian $operatorname{Y}(mathfrak{sl}_{2})$ | | Yikun Zhou
; Yilan Tan
; Limeng Xia
; | | Date: |
10 Jul 2022 | | Abstract: | Let $mathfrak{g}$ be a finite-dimensional simple Lie algebra over
$mathbb{C}$. A $operatorname{Y}(mathfrak{g})$-module is said to be weight if
it is a weight $mathfrak{g}$-module. We give a complete classification of
simple weight modules for $operatorname{Y}(mathfrak{sl}_2)$ which admits a
one-dimensional weight space. We prove that there are four classes of such
modules: finite, highest weight, lowest weight and dense modules. Different
from the classical $mathfrak{sl}_{2}$ representation theory, we show that
there exist a class of $operatorname{Y}(mathfrak{sl}_{2})$ irreducible
modules which have uniformly 2-dimensional weight spaces. | | Source: | arXiv, 2207.04432 | | Services: | Forum | Review | PDF | Favorites | |
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