Affine Yangians and some cosets of non-rectangular $W$-algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914890408525824 |
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| author | Ueda, Mamoru |
| author_facet | Ueda, Mamoru |
| contents | We construct a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(q_u-q_{u+1})$ to the universal enveloping algebra of a $W$-algebra associated with $\mathfrak{gl}(\sum_{s=1}^lq_s)$ and a nilpotent element of type $(1^{q_1-q_2},2^{q_2-q_3},\dots,(l-1)^{q_{l-1}-q_l},l^{q_l})$ by using the coproduct and evaluation map for the affine Yangian and the Miura map for non-rectangular $W$-algebras. As an application, we give a homomorphism from the affine Yangian to some cosets of non-rectangular $W$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine Yangians and some cosets of non-rectangular $W$-algebras Ueda, Mamoru Quantum Algebra Mathematical Physics Rings and Algebras 17B37, 17B69 We construct a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(q_u-q_{u+1})$ to the universal enveloping algebra of a $W$-algebra associated with $\mathfrak{gl}(\sum_{s=1}^lq_s)$ and a nilpotent element of type $(1^{q_1-q_2},2^{q_2-q_3},\dots,(l-1)^{q_{l-1}-q_l},l^{q_l})$ by using the coproduct and evaluation map for the affine Yangian and the Miura map for non-rectangular $W$-algebras. As an application, we give a homomorphism from the affine Yangian to some cosets of non-rectangular $W$-algebras. |
| title | Affine Yangians and some cosets of non-rectangular $W$-algebras |
| topic | Quantum Algebra Mathematical Physics Rings and Algebras 17B37, 17B69 |
| url | https://arxiv.org/abs/2404.18064 |