Double Elliptic Systems: Problems and Perspectives

Abstract

This talk presents a list of problems related to the double-elliptic (Dell) integrable systems with elliptic dependence on both momenta and coordinates. As expected, in the framework of Seiberg-Witten theory the recently discovered explicit self-dual family of 2-particle Dell Hamiltonians provides a perturbative period matrix which is a logarithm of the ratio of the (momentum-space) theta-functions.

arXiv comment18 pages, LaTeX; talk presented at the International Workshop "Supersymmetries and quantum symmetries", Dubna, July 1999

Cited by in corpus (7)

• On Three Dimensional Quiver Gauge Theories and Integrability
• Explicit examples of DIM constraints for network matrix models
• Three-particle Integrable Systems with Elliptic Dependence on Momenta and Theta Function Identities
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Seiberg-Witten curves and double-elliptic integrable systems
• New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
• The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves