On the spectral properties of the quantum cohomology of odd quadrics

TL;DR

This paper investigates the spectral properties of the quantum cohomology of odd quadrics, computing characteristic polynomials and Frobenius-Perron dimensions, and verifies Galkin's lower bound conjecture for these varieties.

Contribution

It provides explicit calculations of spectral data and confirms a conjecture in the context of quantum cohomology of odd quadrics.

Findings

Characteristic polynomial of quantum multiplication operators computed

Frobenius-Perron dimension determined

Galkin's lower bound conjecture verified for OG

Abstract

Let $H^\bullet(\mbox{OG})$ be the quantum cohomology (specialized at $q=1$) of the $2n-1$ dimensional quadric $\mbox{OG}$. We will calculate the characteristic polynomial of the linear operators induced by quantum multiplication in $H^\bullet(\mbox{OG})$ and the Frobenius-Perron dimension. We also check that Galkin's lower bound conjecture holds for $\mbox{OG}$.