A probabilistic approach to the Shintani-Casselman-Shalika formula

Recall that Jacquet's Whittaker function for a group \(G\), in the non-Archimedean case, is essentially proportional to a character of an irreducible representation of the Langlands dual group - a Schur function in the case of \(\text{GL}_n\). This statement is known as the Shintani-Casselman-Shalika formula. In my opinion, Shintani's proof for \(\text{GL}_n\) is remarkably different from the more general proof by Casselman-Shalika. In this talk, I will present a probabilistic proof that is the natural generalisation of Shintani's. It explains the appearance of the Weyl character formula from a reflection principle for random walks.Non UBCUnreviewedAuthor affiliation: Institut de Mathématiques de ToulousePostdoctora