Non-trivial t-intersecting families for symplectic polar spaces

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Let P be a symplectic polar space over a finite field Fq, and Pm denote the set of all m-dimensional subspaces in P. We say a t-intersecting subfamily of Pm is trivial if there exists a t-dimensional subspace contained in each member of this family. In this paper, we determine the structure of the maximum sized non-trivial t-intersecting subfamilies of Pm.