The interplay between quantum integrable models and symmetric functions

par Mickael WHEELER (Univ. de Melbourne)

jeudi 26 nov. 2015, 11:00 → 12:00 Europe/Paris

Auditorium (Annecy-le-Vieux)

Symmetric functions have a long and beautiful history which can be traced back to Cauchy, Jacobi and Weyl. In modern times, symmetric functions have been central in a number of deep pure mathematical problems (including the n! factorial and Macdonald constant term conjectures), in mathematical physics (in soliton theory and the Alday--Gaiotto--Tachikawa correspondence, as just two examples) and in the development of new stochastic processes (most notably the Schur process of Okounkov--Reshetikhin). In this talk I will consider new perspectives on symmetric functions, namely their construction via integrable lattice models, and how this inspires an original approach for the calculation of correlation functions in quantum spin-chains. There are four basic elements in this approach: 1. Expressing correlation functions in terms of form factors, and relating the latter with partition functions in vertex models; 2. Expanding the relevant partition functions in a suitable basis of symmetric functions; 3. Calculating the structure constants for the product of two symmetric functions, to convert bilinear expressions into linear ones; and finally 4. Studying the asymptotics of the participating functions.