Approach to the polynomials related to representation theory from quantum integrable systems

起源于量子可积系统的X=M猜想的研究，使KR晶体张量积的最高权元的母函数与操纵组态的母函数相等，已使D型猜想的目标前进了约80%。对特殊情况E6的研究也开始了。我们还研究了四面体方程与量子群的关系，即三维反射方程解的显式公式，量子坐标环的缠绕子的矩阵元与量子包络代数的PBW基的关系，量子仿射代数的q-振子表示的张量积的2D约化和交织的重合。

The study of X=M conjecture, which originates in quantum integrable systems, equating the generating functions of highest weight elements of the tensor product of KR crystals and rigged configurations has advanced about 80% to the goal for type D. Research for the exceptional case E6 was also begun. However, the study of the relation to LLT polynomial remained to be incomplete.We also studied the relation between tetrahedron equation and quantum groups, namely, explicit formula for the solution to the 3D reflection equation, relation between matrix elements of the intertwiner of the quantum coordinate ring and PBW bases of the quantum enveloping algebra, coincidence of the 2D reduction and the intertwiner of the tensor product of q-oscillator representations of a quantum affine algebra.