Appears in collection : Representations, Probability, and Beyond : A Journey into Anatoly Vershik’s World

Sergei Kerov and Anatoly Vershik discovered and started to study a remarkable group, which is an infinite-dimensional analog of GL(n) over a finite field. This group, denoted by GLB, is locally compact, totally disconnected, and it bears some resemblance with reductive p-adic groups. As demonstrated in a paper by Vadim Gorin, Sergei Kerov, and Anatoly Vershik, the group GLB possesses a rich representation theory. I will describe some results and open problems related to GLB and other similar groups, partly inspired by Kirillov's orbit method. Based on joint work with Cesar Cuenca.