Infinite-level Fock spaces, crystal bases, and tensor product of extremal weight modules of type $A_{+\infty }$

Jae-Hoon Kwon, Soo-Hong Lee

We study the category $\mathcal{C}$ generated by extremal weight modules over $U_q({\mathfrak{gl}}_{>0})$. We show that $\mathcal{C}$ is a tensor category, and give an explicit descr…