本文選題：Leonard對 + Leonard三元組��； 參考：《河北師范大學(xué)》2017年博士論文

【摘要】：Leonard對和Leonard三元組等線性代數(shù)研究對象是研究結(jié)合方案的新理論.這一新理論統(tǒng)稱為Terwilliger代數(shù)的表示理論,并且與李代數(shù)、量子群和數(shù)學(xué)物理有著緊密的聯(lián)系.而以二部圖和幾乎二部圖為組合背景的全二部Leonard對、全二部Leonard三元組以及全幾乎二部Leonard對、全幾乎二部Leonard三元組在Terwilliger代數(shù)的表示理論中顯得更為重要且有意義.本文研究全幾乎二部Leonard對和全幾乎二部Leonard三元組的分類問題.對于給定的Bannai/Ito型全幾乎二部Leonard對和給定的q-Racah型全幾乎二部Leonard對,我們分別構(gòu)作了相應(yīng)的Leonard三元組,得到如下成果:1.證明了只有兩種類型的全幾乎二部Leonard對,分別是q-Racah型和Bannai/Ito型.利用量子包絡(luò)代數(shù)Uq(so_3)的表示理論,在q不是單位根的條件下,給出了q-Racah型全幾乎二部Leonard對的分類.2.利用量子包絡(luò)代數(shù)U(so_3)的表示理論,在q不是單位根的條件下,給出了q-Racah型全幾乎二部Leonard三元組的分類.3.設(shè)K是一個特征為零的代數(shù)閉域.選取K~(d+1)上一個特殊的Bannai/Ito型全幾乎二部的Leonard對(A,A*),我們構(gòu)作了所有的A~ε ∈ Mat_(d+1)(K),使得(A,A*,A~ε)構(gòu)成K~(d+1)上的Leonard三元組.4.設(shè)K是一個特征為零的代數(shù)閉域.選取K~(d+1)上一個特殊的q-Racah型全幾乎二部的Leonard對(A,A*),我們構(gòu)作了所有的A~ε ∈ Mat_(d+1)(K),使得(A,A*,A~ε)構(gòu)成K~(d+1)上的Leonard三元組.
[Abstract]:The research object of linear algebra such as Leonard pair and Leonard triple is a new theory to study the combined scheme.This new theory is called the representation theory of Terwilliger algebra and is closely related to lie algebra, quantum group and mathematical physics.The all-bipartite Leonard pairs, the all-bipartite Leonard triples and the all-almost bipartite Leonard pairs with bipartite and almost bipartite background are more important and meaningful in the representation theory of Terwilliger algebras.In this paper, we study the classification of all almost bipartite Leonard pairs and all almost bipartite Leonard triples.For a given Bannai/Ito type total almost bipartite Leonard pair and a given q-Racah type total almost bipartite Leonard pair, we construct corresponding Leonard triples respectively, and obtain the following result: 1.It is proved that there are only two types of total almost bipartite Leonard pairs, q-Racah type and Bannai/Ito type.By using the representation theory of quantum envelope algebra Uqso _ s _ 3, the classification of almost bipartite Leonard pairs of q-Racah type is given under the condition that Q is not a unit root.By using the representation theory of quantum envelope algebra Uso _ s _ 3, the classification of almost bipartite Leonard triples of q-Racah type. 3 is given under the condition that Q is not a unit root.Let K be an algebraic closed field characterized by zero.In this paper, we select a special Leonard pair of Bannai/Ito type and almost bipartite Leonard to form a Leonard triple. We construct all A ~ 蔚 鈭，

本文編號：1757143