Leonard triples of q-Racah type and their pseudo intertwiners

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• 作者：Paul Terwilliger ^{terwilli@math.wisc.edu}
• 关键词：primary ; 15A21 ; secondary ; 33D45
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：515
• 期：Complete
• 页码：145-174
• 全文大小：523 K
• 卷排序：515

文摘

Let FF denote a field, and let V   denote a vector space over FF with finite positive dimension. Pick a nonzero q∈Fq∈F such that q4≠1q4≠1, and let A,B,CA,B,C denote a Leonard triple on V that has q  -Racah type. We show that there exist invertible W,W′,W″W,W′,W″ in End(V)End(V) such that (i) A commutes with W   and W−1BW−CW−1BW−C; (ii) B   commutes with W′W′ and (W′)−1CW′−A(W′)−1CW′−A; (iii) C   commutes with W″W″ and (W″)−1AW″−B(W″)−1AW″−B. Moreover each of W,W′,W″W,W′,W″ is unique up to multiplication by a nonzero scalar in FF. We show that the three elements W′W,W″W′,WW″W′W,W″W′,WW″ mutually commute, and their product is a scalar multiple of the identity. A number of related results are obtained. We call W,W′,W″W,W′,W″ the pseudo intertwiners   for A,B,CA,B,C.