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Finiteness of cominuscule quantum K -theory

Anders S. BuchPierre-Emmanuel ChaputLeonardo C. MihalceaNicolas Perrin — 2013

Annales scientifiques de l'École Normale Supérieure

The product of two Schubert classes in the quantum K -theory ring of a homogeneous space X = G / P is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on  X . We show that if X is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to  X that take the marked points to general Schubert varieties and whose domains...

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