本文選題：Racah代數(shù) + 既約模　； 參考：《河北師范大學(xué)》2017年碩士論文

【摘要】：設(shè)K為特征為零的代數(shù)閉域,d0,e1,e2為域K中的元.Racah代數(shù)A(d0,e1,e2)是域K上由x,y生成且與d0,e1,e2相關(guān)聯(lián)的一般二次代數(shù),其生成元滿足:x2y-2xyx + yx2 +(xy + yx)+ x2 + d0x + e2 = 0,y2x-2yxy + xy2 +(yx + xy)+ y2 + d0y + e1 = 0.本文利用Leonard對理論,給出了有限維Racah代數(shù)既約模的分類,得到如下結(jié)果:1.我們證明了 Racah代數(shù)生成元x,y在既約模V上的作用是可對角化的,而且這兩個(gè)作用形成一個(gè)V上的Leonard對,分別給出了生成元x,y在既約模V上作用的特征值,并且給出了有限維Racah代數(shù)既約模的分類.2.設(shè)d≥3為整數(shù).對于給定的d + 1維既約A(dA,e1,e2)-模V,我們給出了相應(yīng)的V上的Racah型Leonard對同構(gòu)類.
[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，

本文編號：1973392