Finite-dimensional irreducible representations of twisted loop algebras of the second kind
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910982628966400 |
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| author | Watanabe, Hideya |
| author_facet | Watanabe, Hideya |
| contents | Twisted loop algebras of the second kind are infinite-dimensional Lie algebras that are constructed from a semisimple Lie algebra and an automorphism on it of order at most $2$. They are examples of equivariant map algebras. The finite-dimensional irreducible representations of an arbitrary equivariant map algebra have been classified by Neher--Savage--Senesi. In this paper, we classify the finite-dimensional irreducible representations of twisted loop algebras of the second kind in a more elementary way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-dimensional irreducible representations of twisted loop algebras of the second kind Watanabe, Hideya Representation Theory 17B10, 17B65 Twisted loop algebras of the second kind are infinite-dimensional Lie algebras that are constructed from a semisimple Lie algebra and an automorphism on it of order at most $2$. They are examples of equivariant map algebras. The finite-dimensional irreducible representations of an arbitrary equivariant map algebra have been classified by Neher--Savage--Senesi. In this paper, we classify the finite-dimensional irreducible representations of twisted loop algebras of the second kind in a more elementary way. |
| title | Finite-dimensional irreducible representations of twisted loop algebras of the second kind |
| topic | Representation Theory 17B10, 17B65 |
| url | https://arxiv.org/abs/2506.02379 |