Liouville irregular states of half-integer ranks

We conjecture a set of differential equations that characterizes the Liouville irregular states of half-integer ranks, which extends the generalized AGT correspondence to all the (A₁, A_even) and (A₁, D_odd) types Argyres-Douglas theories. For lower half-integer ranks, our conjecture is verified by deriving it as a suitable limit of a similar set of differential equations for integer ranks. This limit is interpreted as the 2D counterpart of a 4D RG-flow from (A₁, D_2n) to (A₁, D_2n−1). For rank 3/2, we solve the conjectured differential equations and find a power series expression for the irregular state |I^(3/2)〉. For rank 5/2, our conjecture is consistent with the differential equations recently discovered by H. Poghosyan and R. Poghossian.