An introduction to the half-infinite wedge

Rodolfo Rios-Zertuche

Published 2013-08-31, updated 2014-02-27Version 2

After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of the infinite symmetric group. We show how these can be applied to find the limit shapes of several distributions on partitions. We also briefly review the variational methods available to compute these limit shapes.