有限维Racah代数既约模的分类

发布时间：2018-06-03 16:11

  本文选题：Racah代数 + 既约模　； 参考：《河北师范大学》2017年硕士论文

【摘要】：设K为特征为零的代数闭域,d0,e1,e2为域K中的元.Racah代数A(d0,e1,e2)是域K上由x,y生成且与d0,e1,e2相关联的一般二次代数,其生成元满足:x2y-2xyx + yx2 +(xy + yx)+ x2 + d0x + e2 = 0,y2x-2yxy + xy2 +(yx + xy)+ y2 + d0y + e1 = 0.本文利用Leonard对理论,给出了有限维Racah代数既约模的分类,得到如下结果:1.我们证明了 Racah代数生成元x,y在既约模V上的作用是可对角化的,而且这两个作用形成一个V上的Leonard对,分别给出了生成元x,y在既约模V上作用的特征值,并且给出了有限维Racah代数既约模的分类.2.设d≥3为整数.对于给定的d + 1维既约A(dA,e1,e2)-模V,我们给出了相应的V上的Racah型Leonard对同构类.
[Abstract]:Let K be an algebraic closed field with a characteristic of zero, d _ 0e _ 1e _ 2 is the element in the field K, and the Racah algebra A _ f _ d _ 0e _ 1e _ 1e _ 2) is a general quadratic algebra on the field K which is generated by XY and associated with d _ 0e _ 1e _ 2. The generator satisfies: x2y-2xyx yx2 XY y x) x2d0x e2 = 0y 2x-2yxy xy2 yx xyy) y2d0y e1 = 0. In this paper, we give the classification of irreducible modules of finite-dimensional Racah algebras by using Leonard pair theory, and obtain the following result: 1. We prove that the action of Racah algebra generator XY on the reduced module V is diagonalized, and these two actions form a Leonard pair on V. The eigenvalues of the action of the generator XY on the reduced module V are given respectively. The classification of irreducible modules of finite dimensional Racah algebras. Let d 鈮，

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