The $q$-Schur algebras in type $D$, I: fundamental multiplication formulas

Jie Du, Yiqiang Li, Zhaozhao Zhao

By embedding the Hecke algebra ${\check{H}}_q$ of type $D$ into the Hecke algebra $H_{q,1}$ of type $B$ with unequal parameters $(q,1)$, the $q$-Schur algebras $S_q^{\kappa }(n,r)$ of type $D…