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THE BGG RESOLUTION AND THE SPECTRUM OF DIRAC-LAPLACIANS ON NONCOMMUTATIVE LINE BUNDLES
- Speaker(s)
- ELMAR WAGNER
- Affiliation
- Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Mexico
- Language of the talk
- English
- Date
- Oct. 15, 2025, 5:15 p.m.
- Information about the event
- IMPAN - Room 405
- Title in Polish
- THE BGG RESOLUTION AND THE SPECTRUM OF DIRAC-LAPLACIANS ON NONCOMMUTATIVE LINE BUNDLES
- Seminar
- North Atlantic Noncommutative Geometry Seminar
The Bernstein-Gelfand-Gelfand resolution is a powerful tool to define natural elliptic first-order differential operators (Dirac operators) on irreducible flag manifolds. Heckenberger and Kolb showed in 2006 that the same construction applies to noncommutative irreducible flag manifolds defined as quotients of semisimple quantum groups. First, it will be shown on the non-trivial example of the quantum grassmannian Gr(2,4) how the Bernstein-Gelfand-Gelfand resolution leads to an explicit description of the (anti-)holomorphic Dolbeault complex and the Dirac operator on spin bundles. Then I will show how this description facilitates the calculation of the spectrum of the Dirac-Laplacians on line bundles for all noncommutative irreducible flag manifolds of the A-series. (Joint work with Kevin Rodríguez Portillo.)
