我们关于量子仿射gln和仿射q-Schur代数的理论的一篇长篇研究论文被剑桥大学出版社出版的系列丛书London Mathematical Society Lecture Note Series 以专著的形式发表. 在此基础上，我们解决了该书的两个重要遗留问题，相关结果分别发表于2013年的Advances in Mathematics和2015年的Advances in Mathematics. 我们将继续研究量子仿射gln和仿射q-Schur代数, 其中包括仿射A型的Frobenius核, 量子仿射gln的整形式, 量子仿射gln和仿射q-Schur代数的表示理论, modified量子仿射gln的典范基理论, 仿射q-Schur代数的定义关系式等问题. 我们还将研究小q-Schur 代数和无穷小q-Schur 代数的Schur--Weyl对偶问题, 定义关系式等问题.

Our paper about the theory of quantum affine gln and affine q-Schur algebras was published by London Mathematical Society Lecture Note Series, Cambridge University Press, as a monograph. Based on this book, we solved two important remaining problems in this book, the related results was published by Advances in Mathematics in 2013 and 2015. We will continue investigate quantum affine gln and affine q-Schur algebras, including Frobenius Kernel of affine type A, the integral form of quantum affine gln, the representation theory of quantum affine gln and affine q-Schur algebras, the canonical basis theory of modified quantum affine gln, presentation of affine q-Schur algebras, etc. We will also study representation theory of little and infinitesimal q-Schur algebras , including Schur--Weyl duality and presentation of the two algebras, etc.