Generalized Integrability and two-dimensional Gravitation

Abstract

We review the construction of generalized integrable hierarchies of partial differential equations, associated to affine Kac-Moody algebras, that include those considered by Drinfel'd and Sokolov. These hierarchies can be used to construct new models of 2D quantum or topological gravity, as well as new $\mathcal{W}$-algebras.

24 pages, fixed broken tex source

References in corpus (5)

• Hermitian vs. Anti-Hermitian 1-Matrix Models and Their Hierarchies
• Generalized W-algebras and Integrable Hierarchies
• The Lax Operator Approach for the Virasoro and the W-Constraints in the Generalized KdV Hierarchy
• Coadjoint Orbits of the Generalised Sl(2) Sl(3) Kdv Hierarchies
• A note on the Zakharov-Shabat topological model

Cited by in corpus (5)

• Singular Vectors and Topological Theories from Virasoro Constraints via the Kontsevich-Miwa Transform
• Additional Symmetries of Generalized Hierarchies
• Generalized Drinfeld-Sokolov Hierarchies, Quantum Rings, and W-Gravity
• Chiral Rings and Integrable Systems for Models of Topological Gravity
• New Topological Theories and Conjugacy Classes of the Weyl Group