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We study the Witten multiple zeta function associated with the Lie algebra . Our main result shows that its special values at nonnegative integers are always expressible by alternating Euler sums. More precisely, every such special value of weight w at least 2 is a finite ℚ-linear combination of alternating Euler sums of weight w and depth at most 2, except when the only nonzero argument is one of the two last variables, in which case ζ(w−1) is needed.
