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.
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