On affine Deligne-Lusztig varieties for Sp_4(L)

Abstract

In this paper, we study the emptiness/nonemptiness and the dimension formulas of affine Deligne-Lusztig varieties for $S{p}_4(L)$. We mainly calculate the degree of class polynomials for the Iwahori-Hecke algebra of type ${\tilde{C}}_2$. Then, give an explicit description on the emptiness/nonemptiness and dimension formulas of affine Deligne-Lusztig varieties for the group $S{p}_4(L)$.

30 pages