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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Datum:2026
Hauptverfasser: Neguţ, Andrei, Tsymbaliuk, Alexander
Format: Artikel
Sprache:Englisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2026
Online Zugang: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
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Zusammenfassung: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.
DOI:10.3842/umzh.v77i12.9264