q-Inverting pairs of shape 1, 2, 1 |
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| Authors: | Na Kang Bo Hou |
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| Institution: | 1. College of Mathematics and Information Science , Hebei Normal University , Shijiazhuang 050024 , China;2. School of Mathematics and Science , Shijiazhuang University of Economics , Shijiazhuang 050031 , China;3. College of Mathematics and Information Science , Hebei Normal University , Shijiazhuang 050024 , China |
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| Abstract: | Let V denote a vector space with finite positive dimension over an algebraically closed field 𝔽. Let K, K* be a q-inverting pair on V, an ordered pair of invertible linear transformations on V satisfying certain conditions. In this article we study the q-inverting pairs with shape 1, 2, 1. We define a pair of scalars called the parameter pair for K, K*. We give six bases for V and give the action of K, K ?1, K* and (K*)?1 on each of these bases, respectively. We classify the q-inverting pairs of shape 1, 2, 1 in terms of the parameter pairs. We conclude with some trace formulae involving the parameter pair. |
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| Keywords: | split decomposition parameter pair Hessenberg pair |
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