# Moscow Mathematical Journal

Volume 17, Issue 4, October–December 2017 pp. 691–698.

Permutation-Equivariant Quantum K-Theory I. Definitions. Elementary K-Theory of \overline M_{0,n}/*S _{n}*

**Authors**: Alexander Givental (1)

**Author institution:**(1) Department of Mathematics, University of California Berkeley, Berkeley CA 94720, USA

**Summary:**

K-theoretic Gromov–Witten (GW) invariants of a compact
Kähler manifold *X* are defined as super-dimensions of sheaf cohomology of interesting bundles over moduli spaces of *n*-pointed holomorphic
curves in *X*. In this paper, we introduce K-theoretic GW-invariants cognizant of the *S _{n}*-module structure on the sheaf cohomology, induced by
renumbering of the marked points, and compute some of these invariants
for

*X*=pt.

2010 Math. Subj. Class. 14N35.

**Keywords:**K-theory, Gromov–Witten invariants, Schur–Weyl reciprocity, Deligne–Mumford spaces, Veronese curves.

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