Resumen de Components of Springer fibers associated to closed orbits for the symmetric pairs (Sp(2n),Sp(2p)×Sp(2q)) and (SO(2n),GL(n)) I

L. Barchini, Roger Zierau

• For the pairs of complex reductive groups (G, K) = (Sp(2n), Sp(2p)¡¿Sp(2q)) and (SO(2n), GL(n)) components of Springer fibers associated to closed K-orbits in the flag variety B of G are described. The closed K-orbits in B correspond to discrete series representations of GR = Sp(p, q) and SO.(2n). We give an algorithm to compute the associated variety, the closure of a nilpotent K-orbit K ¡¤ f , of each discrete series representation and we describe the structure of the corresponding component of the Springer fiber¥ì.1(f ). The description of these components has applications to the computation of associated cycles of discrete series representations; this is the topic of the sequel to the present article.