New realization of cyclotomic $q$-Schur algebras I

Kentaro Wada

We introduce a Lie algebra ${\mathfrak{g}}_{\mathbf{Q}}(\mathbf{m})$ and an associative algebra ${\mathcal{U}}_{q,\mathbf{Q}}(\mathbf{m})$ associated with the Cartan data of $\mathfrak…