Confluent KZ equations for sl_N with Poincare rank 2 at infinity

Abstract

We construct confluent KZ equations with Poincare rank 2 at infinity for the case of sl_N and the integral representation for the solutions. Hamiltonians of these confluent KZ equations are derived from suitable quantization of dlog tau constructed in the theory of monodromy preserving deformation by Jimbo, Miwa and Ueno. Our confluent KZ equations may be viewed as a quantization of monodromy preserving deformation with Poincare rank 2 at infinity.

27 pages. We change the definition of confluent Verma modules and change Proposition 3.4 and Theorem 3.5 to Conjecture 3.4. We add a proof of Theorem 4.3. Minor change

References in corpus (2)

• Symplectic Manifolds and Isomonodromic Deformations
• Confluent primary fields in the conformal field theory

Cited by in corpus (2)

• Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks
• Topology of irregular isomonodromy times on a fixed pointed curve