A note on extensions of p -adic representations of GL₂(Qₚ)

We compute extension groups in the category of duals of -adic Banach space representations of GL 2 (Q ).Focusing on representations arising from the -adic local Langlands correspondence for generic Galois representations, we classify these extensions completely.These results are then applied to prove the vanishing of extensions between the dual -adic Banach space representations attached to reducible Galois representations and supercuspidal Galois isotypic components of the -adic tale cohomology of the finite level Drinfeld spaces.