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We propose the full system of Baxter Q-functions (QQ-system) for theintegrable spin chains with the symmetry of the $D_r$ Lie algebra. We use thisQQ-system to derive new Weyl-type formulas expressing transfer matrices in allsymmetric and antisymmetric (fundamental) representations through $r+1$ basicQ-functions. Our functional relations are consistent with the Q-operatorsproposed recently by one of the authors and verified explicitly on the level ofoperators at small finite length.

QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains