We describe the structure of the space of second order elliptic differential operators on a homogenous bundle over a compact Lie group. Subject to a technical condition, these operators are homotopic to the Laplacian. The technical condition is further investigated, with examples given where it holds and others where it does not. Since many spectral invariants are also homotopy invariants, these results provide information about the invariants of these operators.

MSC Classifications:

58J70, 43A77 show english descriptions Invariance and symmetry properties [See also 35A30]
Analysis on general compact groups 58J70 - Invariance and symmetry properties [See also 35A30]
43A77 - Analysis on general compact groups

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