The Gindikin-Karpelevich formula in affine type A
Abstract: The Gindikin-Karpelevich formula, due to Langlands, expresses the action of a particular intertwining operator on the spherical vector in a principal series representation as the product over a set of positive roots. In recent work, reinterpreting the result in other algebraic, geometric, and combinatorial settings has been investigated. In joint work with S.-J. Kang, K.-H. Lee, and H. Ryu, we adopt the combinatorial perspective and express the product over positive roots as a sum over a combinatorial realization of a crystal, called generalized Young walls (due to Kim and Shin), when the root system is of affine A type.