A family of tridiagonal pairs Original Research Article

Let F denote a field, and let V denote a vector space of finite positive dimension over F. Let A, A* denote a tridiagonal pair on V of diameter d greater-or-equal, slanted 3. Assume the eigenvalue and dual eigenvalue sequences of A, A* satisfy θi = q2iθ, image for some nonzero scalars θ, θ*, qset membership, variantF, where q is not a root of unity. Assume that not all eigenvalues of A and A* have multiplicity one. Let M and M* denote the subalgebras of End(V) generated by A and A*, respectively, and assume that V = Mv* + M*v for some eigenvectors v* of A* associated with image and v of A associated with θd. We find a nice basis for V and describe the action of A, A* on this basis in terms of six parameters.