In this paper we establish the existence of monads on Cartesian products of projective spaces. We construct vector bundles associated to monads on $\mathbb{ P}^{ a_1}\times\mathbb{ P}^{ a_1}\times\mathbb{ P}^{ a_2}\times\mathbb{ P}^{ a_2}\times\cdots\times\mathbb{ P}^{ a_n}\times\mathbb{ P}^{ a_n}$. Once the monad on $X$ exists the next natural question is if the cohomology vector bundle associated to these monads are simple or not. We study these vector bundles associated to monads on $X$ and prove their stability and simplicity.
Categories: math.AG