![]() This is joint work with Bach Nguyen (Temple University) and Matt Lee (University of Illinois at Chicago). We will conclude with a discussion of the Yangian, its relation to the quantum loop algebra, and some recent work concerning its global Weyl modules. What we will deal with in this course is a special type of 3manifold. Along the way, the utility of highest–weight representations, and of the (local and global) Weyl Modules, in all of these settings will be described. composes along spheres and incompressible tori into pieces that admit uniquely. In this introductory talk, we proceed by example from the classical structure and representation theory of the special linear algebra in dimensions 2 and 3, to that of the corresponding Loop algebras and quantum groups. Particular examples of highest–weight representations of certain infinite–dimensional Lie algebras called the Weyl modules (for loop and quantum algebras) were introduced by Chari and Pressley in 2000. Highest-weight representations play a prominent role in the representation theory of Lie algebras and quantum groups. ![]() Tuck the Figure Eight knot into the fist. The standing end is the section of rope the knot cinches down onto.Highest-weight representations and global Weyl modules: from classical Lie algebras to YangiansĪuthors: Prasad Senesi*, Bach Nguyen and Matt Lee Knot the end you left undisturbed with a Figure Eight knot, and push the ball into the center of the fist. The rope will not hold under heavy strain. However, it’s for light use, not heavy use, such as tying scarves, package parcels, and so forth. The working end of a knot would be the tail, or free end, of the rope that users can manipulate to tie a knot. A square knot is a quick and simple way to join two ropes together. There also are two terms that help someone follow knot-tying directions: working end and standing end.
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