Generating sets of standard modules for $D_4^{(1)}$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908791148118016 |
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| author | Baranović, Ivana Jerkovic, Miroslav Trupčević, Goran |
| author_facet | Baranović, Ivana Jerkovic, Miroslav Trupčević, Goran |
| contents | Let $\widetilde{\mathfrak g}$ be an affine Lie algebra of type $D_4^{(1)}$ and $L(Λ)$ its standard module of level $k$ with highest weight vector $v_Λ$. We define Feigin--Stoyanovsky's type subspace as $W(Λ)=U(\widetilde{\mathfrak g}_{1})\,v_Λ$, where $\widetilde{\mathfrak g}=\widetilde{\mathfrak g}_{-1}\oplus\widetilde{\mathfrak g}_{0}\oplus\widetilde{\mathfrak g}_{1}$ is a $\mathbb{Z}$-gradation of $\widetilde{\mathfrak g}$ associated with a $\mathbb{Z}$-gradation $\mathfrak g=\mathfrak g_{-1}\oplus\mathfrak g_{0}\oplus\mathfrak g_{1}$. Using vertex operator relations, we reduce the Poincaré--Birkhoff--Witt spanning set of $W(Λ)$, and describe it in terms of difference and initial conditions. The spanning set of the whole standard module $L(Λ)$ can be obtained as a limit of the spanning set for $W(Λ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generating sets of standard modules for $D_4^{(1)}$ Baranović, Ivana Jerkovic, Miroslav Trupčević, Goran Quantum Algebra Representation Theory 17B67 (Primary) 17B69, 05A19 (Secondary) Let $\widetilde{\mathfrak g}$ be an affine Lie algebra of type $D_4^{(1)}$ and $L(Λ)$ its standard module of level $k$ with highest weight vector $v_Λ$. We define Feigin--Stoyanovsky's type subspace as $W(Λ)=U(\widetilde{\mathfrak g}_{1})\,v_Λ$, where $\widetilde{\mathfrak g}=\widetilde{\mathfrak g}_{-1}\oplus\widetilde{\mathfrak g}_{0}\oplus\widetilde{\mathfrak g}_{1}$ is a $\mathbb{Z}$-gradation of $\widetilde{\mathfrak g}$ associated with a $\mathbb{Z}$-gradation $\mathfrak g=\mathfrak g_{-1}\oplus\mathfrak g_{0}\oplus\mathfrak g_{1}$. Using vertex operator relations, we reduce the Poincaré--Birkhoff--Witt spanning set of $W(Λ)$, and describe it in terms of difference and initial conditions. The spanning set of the whole standard module $L(Λ)$ can be obtained as a limit of the spanning set for $W(Λ)$. |
| title | Generating sets of standard modules for $D_4^{(1)}$ |
| topic | Quantum Algebra Representation Theory 17B67 (Primary) 17B69, 05A19 (Secondary) |
| url | https://arxiv.org/abs/2601.19415 |