基于racah型距离正则图的一些leonard三元组和racah代数-基础数学专业论文.docxVIP

AbstractBy Abstract By Leonard triple．we mean triple of diagonalizable operators finite-dimensional vector space such that for each operator．there is ordering of eigenbasis for the lected operator with respect to which the other two operators are irreducible tridiagonal． Let C denote the field of complex numbers and let D denote integer at least 3． Let；HⅣ(2D+1，2)denote the halved graph of the(2D+1)一cube with respect to the original P—polynomial structure／to，Rl， ，RD and another Q—polynomial structure 岛，易，置， ，岛，El in terms of the original ones．Let 1／4(4D，2)denote the folded halved graph of the 4D—cube and let 1／4(4D+2，2)denote the folded halved graph of the(4D+2)一cube．Note that they are all distance-regular graphs of Racah type． In this paper we consider the relations between the above three graphs and the Leonard triples the Racah algebra C．Our results described as follows． 1．Fix vertex of百1日Ⅳ(2D+1，2)and let乃denote the corresponding Terwilliger algebra with respect to this vertex．We first construct three elements I工1，埘and撕 of五．Then we show that the triple I工1，珥，撕acts each irreducible TI—module as Leonard triple．Moreover，let冀1 be Racah algebra with its generators and real parameters satisfying certain conditions．We display C—algebra homomorphism from 兵1 to噩． 2．Fix vertex of{／4(4D，2)and let T2 denote the Terwilliger algebra of 1／t(4D，2) with respect to this vertex．We construct three elements u2，啦，啦of T2 and show that the triple％，啦，距not only acts each irreducible T2一module as Leonard triple but also satisfies some very appealing equations．Moreover，let W denote irreducible T2一module with type妒and let勘be Racah algebra with respect to妒．Then there exists a‰-module structure W． 3．Fix vertex of；／4(4D+2，2)and let T3 denote the Terwiniger algebra of j／t(4D+2，2)with respect to this vertex．We construct three elements地，珑，嫣of T3 and show that the triple巩，弼，骟not only acts on each irreducible T3一module as Leonard triple but also satisfies some very appealing equations．Moreover，let W