کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1894790 1533752 2014 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On Mpc-structures and symplectic Dirac operators
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
پیش نمایش صفحه اول مقاله
On Mpc-structures and symplectic Dirac operators
چکیده انگلیسی

We prove that the kernels of the restrictions of the symplectic Dirac operator and one of the two symplectic Dirac–Dolbeault operators on natural sub-bundles of polynomial valued spinor fields are finite dimensional on a compact symplectic manifold. We compute these kernels explicitly for complex projective spaces and show that the remaining Dirac–Dolbeault operator has infinite dimensional kernels on these finite rank sub-bundles. We construct injections of subgroups of the symplectic group (the pseudo-unitary group and the stabiliser of a Lagrangian subspace) in the Mpc group and classify GG-invariant Mpc-structures on symplectic manifolds with a GG-action. We prove a variant of Parthasarathy’s formula for the commutator of two symplectic Dirac-type operators on general symmetric symplectic spaces.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 86, December 2014, Pages 434–466
نویسندگان
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