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

量子可积系统表示论相关多项式的探讨

• 批准号: 23654007
• 负责人: OKADO Masato
• 金额: $ 2.16万
• 依托单位: Osaka City University (2013)Osaka University (2011-2012)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23654007/
• 关键词: 量子群; 表現論; リー環; 可積分系

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.

X = M猜想的研究起源于量子整合系统，将KR晶体张量和操纵配置的最高权重元素的生成功能等同于D的目标。然而，与LLT多项式关系的研究仍然不完整。我们还研究了四面体方程与量子组之间的关系，即明确的公式，以解决3D反射方程，用于3D反射方程，量化环和Pbw eNSERING ALGEN eNGER的矩形元素之间的矩阵元素之间的关系，该元素的互联环和PBW依赖的依赖的依赖eNSEVICN和PBW eNSEVER eNGERAD eNEDER eNGERAD eNGRACERING ALGAR BODENSED ALGRA的依赖的序列依赖的依赖性。量子代数的Q振荡量表示的张量产物的跨区域。

项目成果

Tetrahedron equation and quantum R matrices for infinite dimensional modules of U_q(A^{(1)}_1) and U_q(A^{(2)}_2)

U_q(A^{(1)}_1) 和 U_q(A^{(2)}_2) 无限维模的四面体方程和量子 R 矩阵

• DOI: 10.1088/1751-8113/46/48/485203
• 发表时间: 2013
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: T. Arakawa;T. Kuwabara and F. Malikov;T. Arakawa;T. Arakawa;Tomoyuki Arakawa;T. Arakawa;T. Arakawa;T. Arakawa;T. Arakawa;T. Arakawa;T. Arakawa;T. Arakawa;T. Arakawa;A. Kuniba and M. Okado
• 通讯作者: A. Kuniba and M. Okado

Tetrahedron equation and quantum groups

四面体方程和量子群

• 发表时间: 2013
• 作者: C. Lecouvey;M. Okado and M. Shimozono;T. Arakawa;T. Arakawa;Masato Okado;T. Arakawa;M. Okado
• 通讯作者: M. Okado

Simplicity and similarity of Kirillov-Reshetikhin crystals

基里洛夫-列谢蒂欣晶体的简单性和相似性

• 发表时间: 2013
• 期刊: Contemp. Math
• 作者: A. Kuniba;M. Okado and Y. Yamada;T. Arakawa;M. Okado
• 通讯作者: M. Okado

量子座標環と３次元反射方程式

量子坐标环与三维反射方程

• 作者: 国場敦夫;尾角正人
• 通讯作者: 尾角正人

A solution of the 3D reflection equation from quantized algebra of functions of type B

• DOI: 10.1142/9789814518550_0021
• 发表时间: 2012-10
• 期刊: arXiv: Mathematical Physics
• 作者: A. Kuniba;M. Okado