Cylindric symmetric functions and quantum integrable systems

[摘要] We employ the level-n action of the affine symmetric group to construct cylindric versions of elementary and complete symmetric functions. We identify their expansions in terms of the bases of ordinary elementary and complete symmetric functions with the structure constants of generalised Verlinde algebras. Then we describe statistical vertex models associated to the q-boson model, when evaluated at q=1, and study the interplay between the partition functions of these models and the cylindric symmetric functions introduced above.

[发布机构] University:University of Glasgow;Department:School of Mathematics and Statistics

[关键词] Symmetric functions, cylindric symmetric functions, integrable systems, Yang-Baxter equation, Frobenius Algebras.