Casimir recursion relations for general conformal blocks

Understand

We study the structure of series expansions of general spinning conformal blocks.

• We find that the terms in these expansions are naturally expressed by means of special functions related to matrix elements of Spin(d) representations in Gelfand-Tsetlin basis, of which the Gegenbauer polynomials are a special case.
• We study the properties of these functions and explain how they can be computed in practice.
• We show how the Casimir equation in Dolan-Osborn coordinates leads to a simple one-step recursion relation for the coefficients of the series expansion of general spinning conformal block.