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arXiv · 2406.13160

Global bases for Bosonic extensions of quantum unipotent coordinate rings

Masaki Kashiwara·Myungho Kim·Se-jin Oh·Euiyong Park
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Abstract

In the paper, we establish the global basis theory for the bosonic extension $\widehat{\mathcal{A}}$ associated with an arbitrary generalized Cartan matrix. When $\widehat{\mathcal{A}}$ is of simply-laced finite type, it is isomorphic to the quantum Grothendieck ring of the Hernandez-Leclerc category over a quantum affine algebra. In this case, we show that the $(t,q)$-characters of simple modules in the Hernandez-Leclerc category correspond to the normalized global basis of $\widehat{\mathcal{A}}$.

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Masaki Kashiwara, Myungho Kim, Se-jin Oh, Euiyong Park. 2024-06-19. Global bases for Bosonic extensions of quantum unipotent coordinate rings. https://arxiv.org/abs/2406.13160

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