We study U(N|M) character expectation value with the supermatrix Chern-Simons
theory, known as the ABJM matrix model, with emphasis on its connection to the
knot invariant. This average just gives the half BPS circular Wilson loop
expectation value in ABJM theory, which shall correspond to the unknot
invariant. We derive the determinantal formula, which gives U(N|M) character
expectation values in terms of U(1|1) averages for a particular type of
character representations. This means that the U(1|1) character expectation
value is a building block for all the U(N|M) averages, and in particular, by an
appropriate limit, for the U(N) invariants. In addition to the original model,
we introduce another supermatrix model obtained through the symplectic
transform, which is motivated by the torus knot Chern-Simons matrix model. We
obtain the Rosso-Jones-type formula and the spectral curve for this case.Comment: 1+36 pages, 4 figures, 1 table; typos corrected, minor change
