Permutation-equivariant quantum K-theory III. Lefschetz' formula on ${\overline{M}}_{0,n}/S_n$ and adelic characterization

Abstract

We continue our study of the genus-$0$ permutation-equivariant quantum K-theory of the target $X=pt$, and completely determine the "big J-function" of this theory. The computation is based on the application of Lefschetz' fixed point formula to the action of $S_n$ on ${\overline{M}}_{0,n+1}$. It is an instance of the general "adelic characterization" (which we state at the end with reference to arXiv:1106.3136) of quantum K-theory for any target $X$ in terms of quantum cohomology theory. Yet, some simplifications of non-conceptual nature occur in this example, making it a lucid illustration to the general theory.

11 pages, 1 figure

References in corpus (2)

• The Hirzebruch--Riemann--Roch theorem in true genus-0 quantum K-theory
• Twisted orbifold Gromov-Witten invariants

Cited by in corpus (2)

• Quantum K-theory of grassmannians and non-abelian localization
• $K$-theoretic quasimap wall-crossing