Anzahl theorems in geometry of t-singular classical groups and their applications

摘要

In 1993, Wan obtained Anzahl theorems of subspaces with type in geometry of singular classical groups. As a generalization, we introduce the concept of geometry of t- singular classical groups, and make some newAnzahl theorems of subspaces with type. As applications, we determine the suborbits of subspaces under t- singular classical groups, and compute the lengths and ranks of these suborbits; show that the isotropic subspace poset of F-q(n1+n2+center dot center dot center dot+nt) q has normalized matching property and q- weighted log- concavity ordered by inclusion; and prove that the set of subspaces which are intersection of subspaces in an orbit of totally isotropic subspaces is a partition strongly regularized semilattice ordered by inclusion, and therefore obtain an analog of EKR theorem in this semilattice.