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

X=M猜想的研究起源于量子可积系统，它将KR晶体和组态张量积的最高权元的母函数等同于D型的目标，并开始了对例外情况E6的研究。我们还研究了四面体方程与量子群之间的关系，即三维反射方程的解的显式公式、量子坐标环的交织矩阵元素与量子包络代数的PBW基之间的关系、二维约化的重合与量子仿射代数Q振子表示的张量积交织的关系。

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.