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How to sharpen a tridiagonal pair

open access: yesHow to sharpen a tridiagonal pair
Let denote a field and let V denote a vector space over F with finite positive dimension. We consider a pair of linear transformations A : V → V and A* : V → V that satisfy the following conditions: (i) each of A, A* is diagonalizable; (ii) there exists an ordering {Vi} di=0 of the eigenspaces of A such that A* V i ⊆ Vi-1 + Vi + Vi+1 for 0 ≤ i ≤ d ...
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