New matrix model solutions to the Kac-Schwarz problem

Abstract

We examine the Kac-Schwarz problem of specification of point in Grassmannian in the restricted case of gap-one first-order differential Kac-Schwarz operators. While the pair of constraints satisfying $[{\mathcal{K}}_1,W]=1$ always leads to Kontsevich type models, in the case of $[{\mathcal{K}}_1,W]=W$ the corresponding KP $\tau$-functions are represented as more sophisticated matrix integrals.

19 pages, latex, no figures, contribution to the proceedings of the 29th International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, Germany

References in corpus (6)

• Towards unified theory of $2d$ gravity
• Generalized Kazakov-Migdal-Kontsevich Model: group theory aspects
• Combinatorics of the Modular Group II: the Kontsevich integrals
• $2d$ gravity and matrix models. I. $2d$ gravity
• Unification of All String Models with $c<1$
• Integrable structures in matrix models and physics of 2d-gravity

Cited by in corpus (4)

• Generation of Matrix Models by W-operators
• BGWM as Second Constituent of Complex Matrix Model
• Enumerative geometry, tau-functions and Heisenberg-Virasoro algebra
• Challenges of Matrix Models