  In this paper we define and study a matrix model describing the M-theory
plane wave background with a single Horava-Witten domain wall. In the limit of
infinite mu, the matrix model action becomes quadratic and we can identify the
matrix Hamiltonian with a regularized Hamiltonian for hemispherical membranes
that carry fermionic degrees of freedom on their boundaries. The number of
fermionic degrees of freedom must be sixteen; this condition arises naturally
in the framework of the matrix model. We can also prove the exact E_8 symmetry
of the spectrum around the membrane vacua at infinite mu, which arises as a
current algebra at level one just as in the heterotic string. We also find the
full E_8 gauge multiplet as well as the multiple-gluon states, carried by
collections of hemispherical membranes. Finally we discuss the dual description
of the hemispherical membranes in terms of spherical fivebranes immersed in the
domain wall; we identify the correct vacuum of the matrix model and make some
preliminary comparisons with the (1,0) superconformal field theory.
