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Simplicity of stable principal sheaves
Author(s) -
Biswas Indranil,
Gómez Tomás L.
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm116
Subject(s) - mathematics , sheaf , pure mathematics , principal bundle , holomorphic function , vector bundle , principal (computer security) , algebraic group , hermitian matrix , linear algebraic group , complex manifold , connection (principal bundle) , algebra over a field , algebraic number , mathematical analysis , geometry , computer science , operating system
Let M be a compact connected Kähler manifold, and let G be a connected complex reductive linear algebraic group. We prove that a principal G ‐sheaf on M admits an admissible Einstein–Hermitian connection if and only if the principal G ‐sheaf is polystable. Using this it is shown that the holomorphic sections of the adjoint vector bundle of a stable principal G ‐sheaf on M are given by the center of the Lie algebra of G . The Bogomolov inequality is shown to be valid for polystable principal G ‐sheaves.