I believe the answer is yes. There are perhaps several ways to see this, but a decent reference is the book "Affine Flag Manifolds and Principal Bundles" by Schmitt. It contains an article called "Quantization of Hitchin’s Integrable System and the Geometric Langlands Conjecture" by T.L. Gomez. Your answer can be found near the beginning of Section 4.1.
Peter Crooks
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