Reflection Equation Day

27th of April 2016

School of Mathematics and Statistics, Newcastle University

Schedule

• 2:30-3:30
  • Dimitri Gurevich (Valenciennes University, France)
  • Quantum matrix algebras and braided Yangians
  • ABSTRACT: By quantum matrix algebras I mean algebras related to quantum groups and close in a sense to that Mat(m). These algebras have numerous applications. In particular, by using them (more precisely, the so-called reflection equation algebras) we succeeded in defining partial derivatives on the enveloping algebras U(gl(m)). This enabled us to develop a new approach to Noncommutative Geometry: all objects of this type geometry are deformations of their classical counterparts. Also, with the help of the reflection equation algebras we introduced the notion of braided Yangians, which are natural generalizations of the usual ones and have many beautiful properties.
  • Slides
• 3:30-4:00
  • Coffee break, HERB.3.20 (Library)
• 4:00-4:45
  • Vidas Regelskis (The University of York)
  • Towards a classification of trigonometric reflection matrices. Part 1.
  • ABSTRACT: Analogous to the role of the Yang-Baxter equation in representation theory of quantum groups, the reflection equation appears naturally in the representation theory of their coideal subalgebras. In the first part of this joint presentation we will discuss the problem of classifying solutions of the reflection equation in the context of Drinfeld-Jimbo quantum groups, yielding trigonometric parameter-dependent reflection matrices. Following this, we will explain how a class of coideal quantum groups given by quantum symmetric Kac-Moody pairs can be used to obtain a classification of trigonometric reflection matrices.
  • Notes
• 5:00-5:45
  • Bart Vlaar (The University of Nottingham)
  • Towards a classification of trigonometric reflection matrices. Part 2.
  • ABSTRACT: We discuss the approach set out in the first part of this talk in more detail. We highlight some interesting aspects of the classification, which in its current form is restricted to so-called quasistandard quantum symmetric pair coideal subalgebras of affine quantum groups of classical (A, B, C, D) Lie type. The classification is simplified, and structured, by two types of equivalence of reflection matrices, rotation and dressing, both of which are induced by the notion of equivalence of coideal subalgebras (in terms of Hopf algebra automorphisms). Many concepts will be illustrated in terms of Satake diagrams, which are known to classify the relevant coideal subalgebras.
  • Slides

The talks will be held at the School of Mathematics and Statistics at Newcastle University, Herschel building room HERB.4.TR3. All are welcome. Here are some maps of the campus and the city center. For further information please email martina.balagovic@ncl.ac.uk.