Extended Schur’s <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2453" altimg="si5.svg"><mml:mi>Q</mml:mi></mml:math>-functions and the full Kostant–Toda hierarchy on the Lie algebra of type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2458" altimg="si6.svg"><mml:mi>D</mml:mi></mml:math>

The full Kostant–Toda hierarchy on a semisimple Lie algebra is system of Lax equations, in which the flows are determined by gradients Chevalley invariants. This paper concerned with even orthogonal algebra. By using Pfaffian matrix as one invariants, we construct an explicit form flow associated to this invariant. As main result, introduce extension Schur’s Q-functions time variables, and use them give all polynomial τ-functions hierarchy.