ICTS:30030

Video URL

[ONLINE] Colored vertex models, orthogonal functions and probability - II

[ONLINE] Colored vertex models, orthogonal functions and probability - II

(2024). [ONLINE] Colored vertex models, orthogonal functions and probability - II. SciVideos. https://youtube.com/live/9lKgtqDMfFw

[ONLINE] Colored vertex models, orthogonal functions and probability - II. SciVideos, Oct. 24, 2024, https://youtube.com/live/9lKgtqDMfFw 

          @misc{ scivideos_ICTS:30030,
            doi = {},
            url = {https://youtube.com/live/9lKgtqDMfFw},
            author = {},
            keywords = {},
            language = {en},
            title = {[ONLINE] Colored vertex models, orthogonal functions and probability - II},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:30030 see, \url{https://scivideos.org/icts-tifr/30030}}
          }
Michael Wheeler
Talk numberICTS:30030
Source RepositoryICTS-TIFR
Source EventDiscrete integrable systems: difference equations, cluster algebras and probabi…
Collection

Abstract

A colored vertex model is a solution of the Yang--Baxter equation based on a higher-rank Lie algebra. These models generalize the famous six-vertex model, which may be viewed in terms of osculating lattice paths, to ensembles of colored paths. By studying certain partition functions within these models, one may define families of multivariate rational functions (or polynomials) with remarkable algebraic features. In these lectures, we will examine a number of these properties:
(a) Exchange relations under the Hecke algebra;
(b) Infinite summation identities of Cauchy-type;
(c) Orthogonality with respect to torus scalar products;
(d) Multiplication rules (combinatorial formulae for structure constants).

Our aim will be to show that all such properties arise very naturally within the algebraic framework provided by the vertex models. If time permits, applications to probability theory will be surveyed.