Abstract
The lattice model of the Weil representation over non-archimedean local field of odd residual characteristic has been known for decades, and is used to prove the Howe duality conjecture for unramified dual pairs when the residue characteristic is odd. In this talk, we will talk on how to modify the lattice model of the Weil representation so that it is defined independently of the residue characteristic. Although to define the lattice model alone is not enough to prove the Howe duality conjecture for even residual characteristic, we will propose a couple of conjectural lemmas which imply the Howe duality conjecture for unramified dual pairs independently of the residue characteristic. Also those two lemmas can be proven for certain cases, which allow us to prove (a version of) the Howe duality conjecture for the even-orthogonal-symplectic dual pair of equal rank for a certain class of representations, independently of the residue characteristic.