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

          @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}}
          }
          

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.