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I am trying to read and understand (parts of) Gaitsgory's “Outline of the proof of the Geometric Langlands conjecture for GL(2)” [arXiv link]. In Section 6.4.8 he states "Property Ei", which basically asserts that the Eisenstein series functors on the spectral and automorphic sides correspond to each other. However the asserted commutative diagram contains twists by a line bundles $\check{\mathfrak{l}}_{M,G}$ and a D-module $\mathfrak{l}_{M,G}$.

What is the meaning of $\check{\mathfrak{l}}_{M,G}$ and $\mathfrak{l}_{M,G}$?

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