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math.RT2024
Braid symmetries on bosonic extensions
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
We introduce a family of automorphisms on the bosonic extension of arbitrary type and show that they satisfy the braid relations. They preserve the global basis and the crystal bas…
math.RT2024
Global bases for Bosonic extensions of quantum unipotent coordinate rings
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
In the paper, we establish the global basis theory for the bosonic extension associated with an arbitrary generalized Cartan matrix. When $\widehat{\mathcal…
math.QA2024
PBW theory for Bosonic extensions of quantum groups
Se-jin Oh, Euiyong Park
In this paper, we develop the PBW theory for the bosonic extension $\qbA{\g}$ of a quantum group $\mathcal{U}_q(\g)$ of \emph{any} finite type. When $\g$ belongs to the class of \e…