Linear relations supplementing BKP for the Kontsevich matrix model with even potential

TL;DR

This paper demonstrates that for the Kontsevich matrix model with even potential, moments satisfy simpler linear relations organized by Schur Q-functions, supplementing the previously known quadratic BKP relations.

Contribution

It introduces linear relations for moments in the Kontsevich matrix model with even potential, simplifying the quadratic BKP relations previously established.

Findings

Moments satisfy linear relations for even potentials.

Linear relations are organized by elementary Schur Q-functions.

Simplifies the understanding of relations in the matrix model.

Abstract

With G. Borot we have previously proved that moments of the Kontsevich matrix model with arbitrary potential satisfy quadratic BKP relations. In this note we show that, for even potential, these moments also satisfy simpler linear relations, which are organised by elementary Schur Q-functions.