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arXiv · 1911.12773

A Chevalley formula for semi-infinite flag manifolds and quantum K-theory (Extended abstract)

Cristian Lenart·Satoshi Naito·Daisuke Sagaki
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Abstract

We give a combinatorial Chevalley formula for an arbitrary weight, in the torus-equivariant K-theory of semi-infinite flag manifolds, which is expressed in terms of the quantum alcove model. As an application, we prove the Chevalley formula for anti-dominant fundamental weights in the (small) torus-equivariant quantum K-theory of the flag manifold G/B; this has been a longstanding conjecture about the multiplicative structure of the mentioned quantum K-theory. Moreover, in type A, we prove that the so-called quantum Grothendieck polynomials indeed represent Schubert classes in the (non-equivariant) quantum K-theory of the corresponding flag manifold.

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Cristian Lenart, Satoshi Naito, Daisuke Sagaki. 2019-11-28. A Chevalley formula for semi-infinite flag manifolds and quantum K-theory (Extended abstract). https://arxiv.org/abs/1911.12773

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