K-Theoretic Gromov–Witten Invariants Of Line Degrees On Flag Varieties

Document Type

Article

Publication Date

11-30-2024

Published In

International Journal Of Modern Physics A

Abstract

A homology class d∈H2(X,Z) of a complex flag variety X=G∕P is called a line degree if the moduli space ¯¯¯¯¯M0,0(X,d) of 0-pointed stable maps to X of degree d is also a flag variety G∕P'. We prove a quantum equals classical formula stating that any n-pointed (equivariant, K-theoretic, genus zero) Gromov–Witten invariant of line degree on X is equal to a classical intersection number computed on the flag variety G∕P'. We also prove an n-pointed analogue of the Peterson comparison formula stating that these invariants coincide with Gromov–Witten invariants of the variety of complete flags G∕B. Our formulas make it straightforward to compute the big quantum K-theory ring QKbig(X) modulo the ideal ⟨Qd⟩ generated by degrees d larger than line degrees.

Keywords

Gromov–Witten invariants, flag varieties, big quantum K-theory

Link to Full Text

Share

COinS