PIRSA:17020020

Nahm transformation for parabolic harmonic bundles on the projective line with regular residues

Szabo, S. (2017). Nahm transformation for parabolic harmonic bundles on the projective line with regular residues. Perimeter Institute. https://pirsa.org/17020020

Szabo, Szilard. Nahm transformation for parabolic harmonic bundles on the projective line with regular residues. Perimeter Institute, Feb. 13, 2017, https://pirsa.org/17020020 

          @misc{ pirsa_PIRSA:17020020,
            doi = {10.48660/17020020},
            url = {https://pirsa.org/17020020},
            author = {Szabo, Szilard},
            keywords = {Mathematical physics},
            language = {en},
            title = {Nahm transformation for parabolic harmonic bundles on the projective line with regular residues},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {feb},
            note = {PIRSA:17020020 see, \url{https://pirsa.org}}
          }

Szilard Szabo Budapest University of Technology and Economics

DOI 10.48660/17020020
Collection
Talk Type Conference
Subject

Abstract

I will define a generalization of the classical Laplace transform for D-modules on the projective line to parabolic harmonic bundles with finitely many logarithmic singularities with regular residues and one irregular singularity, and show some of its properties. The construction involves on the analytic side L2-cohomology, and it has algebraic de Rham and Dolbeault interpretations using certain elementary modifications of complexes. We establish stationary phase formulas, in patricular a transformation rule for the parabolic weights. In the regular semi-simple case we show that the transformation is a hyper-Kaehler isometry.