A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra
We first present a filtration on the ring Ln of Laurent polynomials such that the direct sum decomposition of its associated graded ring grLn agrees with the direct sum decomposition of grLn, as a module over the complex general linear Lie algebra gl(n), into its simple submodules. Next, generalizin...
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| Date: | 2021 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2021
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188715 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra / C. Choi, S. Kim, H. Seo // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 1. — С. 9–32. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We first present a filtration on the ring Ln of Laurent polynomials such that the direct sum decomposition of its associated graded ring grLn agrees with the direct sum decomposition of grLn, as a module over the complex general linear Lie algebra gl(n), into its simple submodules. Next, generalizing the simple modules occurring in the associated graded ring grLn, we give some explicit constructions of weight multiplicity-free irreducible representations of gl(n). |
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