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Finiteness of cominuscule quantum $K$ -theory

Anders S. Buch; Pierre-Emmanuel Chaput; Leonardo C. Mihalcea; Nicolas 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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