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RESEARCH ARTICLE
A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra
C. Choia, S. Kima, H. Seob a Department of Mathematics, Korea University, 145 Anam-ro Seongbuk-gu, Seoul 02841, South Korea
b Department of Mathematics, University of Maryland, William E. Kirwan Hall, 4176 Campus Drive, College Park, MD 20742-4015, USA
Abstract:
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:
Laurent polynomial, filtration, general linear Lie algebra, weight module.
Received: 13.12.2018 Revised: 24.02.2021
Citation:
C. Choi, S. Kim, H. Seo, “A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra”, Algebra Discrete Math., 32:1 (2021), 9–32
Linking options:
https://www.mathnet.ru/eng/adm804 https://www.mathnet.ru/eng/adm/v32/i1/p9
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Abstract page: | 38 | Full-text PDF : | 36 | References: | 13 |
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