# Dynamical Quantum Algebras, Quantum Function Algebras, and their Representations

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Nigel Higson, Mathieu Stiénon, Ping Xu.

**Speaker:** Bharath Narayanan, Penn State

**Abstract:** I will explain the representation theory for quantized function algebras and dynamical quantum algebraic structures on a simple Lie group. Dynamical Quantum Algebras are a class of important noncommutative algebras, originating in exactly solvable models in statistical mechanics and conformal field theory. They have also proven to be very useful for easily veriftying many identities of hypergeometric series. Quantized function algebras, commonly known as the quantum matrix algebras, are quantum versions of usual coordinate rings of Lie groups. They can also be viewed as degenerations of the dynamical algebras, by sending the spectral parameter to infinity, and have numerous applications in q-series, noncommutative geometry and mathematical physics. After an introduction to the basic characters of our investigation - the R-matrices, Yang Baxter equations, Hopf Algebroids and Dynamical Representations, we will explore important relationships between the different algebras and their irreducible representations, to discover a surprising result, known as â€œSelf-Dualityâ€. The examples of sl2 and sl3 will be presented in detail since more or less all of the important ideas can be illustrated explicitly in these 2 cases.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 04/23/2013

**Time:** 2:30pm - 3:30pm