Stable maps, Q-operators and category O
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866929564636151808 |
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| author | Hernandez, David |
| author_facet | Hernandez, David |
| contents | Motivated by Maulik-Okounkov stable maps associated to quiver varieties, we define and construct algebraic stable maps on tensor products of representations in the category O of the Borel subalgebra of an arbitrary untwisted quantum affine algebra. Our representation-theoretical construction is based on the study of the action of Cartan-Drinfeld subalgebras. We prove the algebraic stable maps are invertible and depend rationally on the spectral parameter. As an application, we obtain new R-matrices in the category O and we establish that a large family of simple modules, including the prefundamental representations associated to Q-operators, generically commute as representations of the Cartan-Drinfeld subalgebra. We also establish categorified QQ*-systems in terms of the R-matrices we construct. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_02843 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Stable maps, Q-operators and category O Hernandez, David Representation Theory Quantum Algebra Motivated by Maulik-Okounkov stable maps associated to quiver varieties, we define and construct algebraic stable maps on tensor products of representations in the category O of the Borel subalgebra of an arbitrary untwisted quantum affine algebra. Our representation-theoretical construction is based on the study of the action of Cartan-Drinfeld subalgebras. We prove the algebraic stable maps are invertible and depend rationally on the spectral parameter. As an application, we obtain new R-matrices in the category O and we establish that a large family of simple modules, including the prefundamental representations associated to Q-operators, generically commute as representations of the Cartan-Drinfeld subalgebra. We also establish categorified QQ*-systems in terms of the R-matrices we construct. |
| title | Stable maps, Q-operators and category O |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/1902.02843 |