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In this paper, we study the emptiness/nonemptiness and the dimension formulasof affine Deligne-Lusztig varieties for $Sp_4(L)$. We mainly calculate thedegree of class polynomials for the Iwahori-Hecke algebra of type$\widetilde{C}_2$. Then, give an explicit description on theemptiness/nonemptiness and dimension formulas of affine Deligne-Lusztigvarieties for the group $Sp_4(L)$.

On affine Deligne-Lusztig varieties for Sp_4(L)