Mirror symmetry on levels of non-abelian Landau--Ginzburg orbifolds

TL;DR

This paper explores a conjectured mirror symmetry between dual Landau-Ginzburg orbifolds, focusing on invariants like Euler characteristics and zeta functions, and provides partial evidence supporting this conjecture.

Contribution

It introduces a new conjecture that mirror symmetry extends to each level of orbifold invariants in non-abelian Landau-Ginzburg models and offers partial results supporting it.

Findings

Partial results support the mirror symmetry conjecture for orbifold invariants.

The study extends mirror symmetry to conjugacy classes of permutations (levels).

Analysis of orbifold Euler characteristics, zeta functions, and E-functions in dual pairs.

Abstract

We consider the Berglund-H\"ubsch-Henningson-Takahashi duality of Landau-Ginzburg orbifolds with a symmetry group generated by some diagonal symmetries and some permutations of variables. We study the orbifold Euler characteristics, the orbifold zeta functions and the orbifold E-functions of such dual pairs. We conjecture that we get a mirror symmetry between these invariants even on each level, where we call level the conjugacy class of a permutation. We support this conjecture by giving partial results for each of these invariants.