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ファイル | 記述 | サイズ | フォーマット | |
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fms.2022.15.pdf | 610.01 kB | Adobe PDF | 見る/開く |
タイトル: | Urod algebras and Translation of W-algebras |
著者: | Arakawa, Tomoyuki https://orcid.org/0000-0002-9020-3498 (unconfirmed) Creutzig, Thomas Feigin, Boris |
著者名の別形: | 荒川, 知幸 |
キーワード: | 17B65: Infinite-dimensional Lie (super)algebras 17B69: Vertex operators; vertex operator algebras and related structures |
発行日: | 2022 |
出版者: | Cambridge University Press (CUP) |
誌名: | Forum of Mathematics, Sigma |
巻: | 10 |
論文番号: | e33 |
抄録: | In this work, we introduce Urod algebras associated to simply laced Lie algebras as well as the concept of translation of W-algebras. Both results are achieved by showing that the quantum Hamiltonian reduction commutes with tensoring with integrable representations; that is, for V and L an affine vertex algebra and an integrable affine vertex algebra associated with g, we have the vertex algebra isomorphism H⁰[DS, f](V⊗L)≅H⁰[DS, f] ((V)⊗L, where in the left-hand-side the Drinfeld–Sokolov reduction is taken with respect to the diagonal action of ˆg on V⊗L. The proof is based on some new construction of automorphisms of vertex algebras, which may be of independent interest. As corollaries, we get fusion categories of modules of many exceptional W-algebras, and we can construct various corner vertex algebras. A major motivation for this work is that Urod algebras of type A provide a representation theoretic interpretation of the celebrated Nakajima–Yoshioka blowup equations for the moduli space of framed torsion free sheaves on ℂℙ² of an arbitrary rank. |
著作権等: | © The Author(s), 2022. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. |
URI: | http://hdl.handle.net/2433/274908 |
DOI(出版社版): | 10.1017/fms.2022.15 |
出現コレクション: | 学術雑誌掲載論文等 |
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