On the geometry of some unitary Riemann surface braid group representations and Laughlin-type wave functions

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Abstract

In this note we construct the simplest unitary Riemann surface braid group representations geometrically by means of stable holomorphic vector bundles over complex tori and the prime form on Riemann surfaces. Generalised Laughlin wave functions are then introduced. The genus one case is discussed in some detail also with the help of noncommutative geometric tools, and an application of Fourier-Mukai-Nahm techniques is also given, explaining the emergence of an intriguing Riemann surface braid group duality.
Original languageEnglish
Pages (from-to)120-140
Number of pages21
JournalJournal of Geometry and Physics
Volume2015
Publication statusPublished - 2015

Keywords

  • Riemann surface braid groups, stable holomorphic vector bundles, prime form, Laughlin wave functions, noncommutative geometry.

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