تقرير
Braid group action on quantum virtual Grothendieck ring through constructing presentations
العنوان: | Braid group action on quantum virtual Grothendieck ring through constructing presentations |
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المؤلفون: | Jang, Il-Seung, Lee, Kyu-Hwan, Oh, Se-jin |
سنة النشر: | 2023 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Quantum Algebra, 13F60, 17B37, 17B10, 17B67, 18N25 |
الوصف: | As a continuation of \cite{JLO1}, we investigate the quantum virtual Grothendieck ring $\frakK_q(\g)$ associated with a finite dimensional simple Lie algebra $\g$, especially of non-simply-laced type. We establish an isomorphism $\Uppsi_Q$ between the heart subring $\frakK_{q,Q}(\g)$ of $\frakK_q(\g)$ associated with a Dynkin quiver $Q$ of type $\g$ and the unipotent quantum coordinate algebra $\calA_q(\n)$ of type $\g$. This isomorphism and the categorification theory via quiver Hecke algebras enable us to obtain a presentation of $\frakK_q(\g)$, which reveals that $\frakK_q(\g)$ can be understood as a boson-extension of $\calA_q(\n)$. Then we show that the automorphisms, arising from the reflections on Dynkin quivers and the isomorphisms $\Uppsi_Q$, preserve the canonical basis $\sfL_q$ of $\frakK_q(\g)$. Finally, we prove that such automorphisms produce a braid group $B_\g$ action on $\frakK_q(\g)$. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2305.19471 |
رقم الأكسشن: | edsarx.2305.19471 |
قاعدة البيانات: | arXiv |
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