Fusion and specialization for type ADE shuffle algebras
UDC 512.5 Root vectors in quantum groups (of finite type) are generalized to fused currents in quantum loop groups [J. Ding, S. Khoroshkin, Transform. Groups, 5, №1, 35–59 (2000)]. We construct fused currents as duals to specialization maps of the corresponding shuffle algebras [B. Enriquez, Transf...
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| Дата: | 2026 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/9264 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 512.5
Root vectors in quantum groups (of finite type) are generalized to fused currents in quantum loop groups [J. Ding, S. Khoroshkin, Transform. Groups, 5, №1, 35–59 (2000)]. We construct fused currents as duals to specialization maps of the corresponding shuffle algebras [B. Enriquez, Transform. Groups, 5, №2, 111–120 (2000), B. Enriquez, J. Lie Theory, 13, №1, 21–64 (2003), and B. Feigin, A. Odesskii, NATO Sci., Ser. II, Math. Phys. Chem., 35 (2001)] for the ADE types; an approach, which has a potential for generalization to arbitrary Kac–Moody types. Both root vectors and fused currents depend on a convex order of the positive roots and, in the present paper, we choose the Auslander–Reiten order [C. Ringel, J. reine und angew. Math., 470, 51–88 (1996)] corresponding to the orientation of the ADE-type Dynkin diagram. |
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| DOI: | 10.3842/umzh.v77i12.9264 |