Quantum ${\mathfrak{gl}}_{\infty }$, infinite $q$-Schur algebras and their representations

Jie Du, Qiang Fu

In this paper, we investigate the structure and representations of the quantum group $\mathbf{U}(\infty )={\mathbf{U}}_{\upsilon }({\mathfrak{gl}}_{\infty })$. We will present a realization for…