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Global basis theory reveals connections between bosonic extensions and quantum coordinate rings, indicating a new mathematical framework.
In the paper, we establish the global basis theory for the bosonic extension associated with an arbitrary symmetrizable generalized Cartan matrix. When is of simply laced finite type, is isomorphic to the quantum Grothendieck ring of the Hernandez–Leclerc category over a quantum affine algebra of untwisted type. In this case, we show that the ‐characters of simple modules in correspond to the normalized global basis of .
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Kashiwara et al. (2025) studied this question.
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