Random polymer models and classical groups

量子物理学・ナノサイエンス第246回セミナー / 東京確率論セミナー

概要

The relation between polymer models at zero temperature and characters of the general linear group GLn(R) has been known since the first breakthroughs in the field around the KPZ universality through the works of Johansson, Baik, Rains, Okounkov and others. Later on, geometric liftings of the GLn(R) characters ap-peared in the study of positive temperature polymer models in the form of GLn(R)-Whittaker functions. In this talk I will describe joint works with E. Bisi where we have established that Whittaker functions associated to the orthogonal group SO_2n+1(R) can be used to describe laws of positive temperature polymers when their end point is free to lie on a line. Going back to zero temperature, we will also see that characters of other classical groups such as SO_2n+1(R),Sp_2n(R),SO_2n(R) do play a role in describing laws of polymers in various geometries. This occurence might be surprising given the length of time these models have been studied.

• 量子物理学・ナノサイエンス第246回セミナー

• 量子物理学・ナノサイエンス先端研究センター 主催
• 東京確率論セミナー / 東京工業大学理学院・物理学系 共催