Geodesic
A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra
Algebra and discrete mathematics, Tome 32 (2021) no. 1, pp. 9-32

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We first present a filtration on the ring $L_n$ of Laurent polynomials such that the direct sum decomposition of its associated graded ring $\operatorname{gr} L_n$ agrees with the direct sum decomposition of $\operatorname{gr} L_n$, as a module over the complex general linear Lie algebra $\mathfrak{gl}(n)$, into its simple submodules. Next, generalizing the simple modules occurring in the associated graded ring $\operatorname{gr} L_n$, we give some explicit constructions of weight multiplicity-free irreducible representations of $\mathfrak{gl}(n)$.
Keywords: general linear Lie algebra, weight module.
Mots-clés : Laurent polynomial, filtration 
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     author = {C. Choi and S. Kim and H. Seo},
     title = {A filtration on the ring of {Laurent} polynomials and representations of the general linear {Lie} algebra},
     journal = {Algebra and discrete mathematics},
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     publisher = {mathdoc},
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     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a1/}
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C. Choi; S. Kim; H. Seo. A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra. Algebra and discrete mathematics, Tome 32 (2021) no. 1, pp. 9-32. http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a1/