Explicit construction of unitary irreps of the 2D Euclidean and Poincaré groups via Mackey induction yields matrix elements in Bessel functions for the Euclidean case and modified Bessel/Hankel functions plus rigged Hilbert spaces for the Poincaré case.
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Representations of the D=2 Euclidean and Poincar\'e groups
Explicit construction of unitary irreps of the 2D Euclidean and Poincaré groups via Mackey induction yields matrix elements in Bessel functions for the Euclidean case and modified Bessel/Hankel functions plus rigged Hilbert spaces for the Poincaré case.