Theorem 1.5. Assume that g is simply laced. Then the functions J α satisfy the following recursive relation: Here β → β * stands for the natural isomorphism between the coroot lattice of g and its root lattice. The equation (1.3) appears in [14] , where the authors show that (1.3) holds precisely if and only if the generating function of the J α 's is an eigen-function of the above-mentioned quantum difference Toda system. Thus, Theorem 1.5 and the main result of [14] imply the following. 1 In

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... act, in [24] the authors work with an arbitrary smooth projective variety X instead of B g . In this case the definition of J α is similar, however technically the pushforward must be taken with respect to certain virtual fundamental cycle in K-theory. In the case when X is a homogeneous space of a linear algebraic group, this reduces to the usual pushforward. License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use SEMI-INFINITE SCHUBERT VARIETIES AND QUANTUM K-THEORY 1149 Corollary 1.6. Let g be simply laced. Then the equivariant K-theoretic J-function of B g is an eigen-function of the quantum difference Toda integrable system associated with g.