  We study finite-dimensional representations of hyper loop algebras, i.e., the
hyperalgebras over an algebraically closed field of positive characteristic
associated to the loop algebra over a complex finite-dimensional simple Lie
algebra. The main results are the classification of the irreducible modules, a
version of Steinberg's Tensor Product Theorem, and the construction of positive
characteristic analogues of the Weyl modules as defined by Chari and Pressley
in the characteristic zero setting. Furthermore, we start the study of
reduction modulo p and prove that every irreducible module of a hyper loop
algebra can be constructed as a quotient of a module obtained by a certain
reduction modulo p process applied to a suitable characteristic zero module. We
conjecture that the Weyl modules are also obtained by reduction modulo p. The
conjecture implies a tensor product decomposition for the Weyl modules which we
use to describe the blocks of the underlying abelian category.
