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The space of local operators in the SU(2) invariant Thirring model (SU(2)ITM) is studied by the form factor bootstrap method. By constructing sets ofform factors explicitly we define a susbspace of operators which has the samecharacter as the level one integrable highest weight representation of\hat{sl_2}. This makes a correspondence between this subspace and the chiralspace of local operators in the underlying conformal field theory, the su(2)Wess-Zumino-Witten model at level one.Comment: 19 pages, typos are corrected, Accepted for publication in Comm.  Math. Phy

The Chiral Space of Local Operators in SU (2)-Invariant Thirring Model