Minimal Affinizations of Representations of Quantum Groups: the simply--laced case

We continue our study of minimal affinizations for algebras of type D, E.Comment: 25 page

On multigraded generalizations of Kirillov-Reshetikhin modules

We study the category of Z^l-graded modules with finite-dimensional graded pieces for certain Z+^l-graded Lie algebras. We also consider certain Serre subcategories with finitely many isomorphism classes of simple objects. We construct projective resolutions for the simple modules in these categories and compute the Ext groups between simple modules. We show that the projective covers of the simple modules in these Serre subcategories can be regarded as multigraded generalizations of Kirillov-Reshetikhin modules and give a recursive formula for computing their graded characters

Extended T-systems

We use the theory of q-characters to establish a number of short exact sequences in the category of finite-dimensional representations of the quantum affine groups of types A and B. That allows us to introduce a set of 3-term recurrence relations which contains the celebrated T-system as a special case.Comment: 36 pages, latex; v2: version to appear in Selecta Mathematic

Nobel laureate Robert E. Lucas, Jr.; architect of modern macroeconomics

In 1995, Robert E. Lucas, Jr., was awarded the Nobel Prize in Economic Sciences. This review places Lucas’ work in a historical context and evaluates the effect of this work on the economics profession. Lucas’ central contribution is that he developed and applied economic theory to answer substantive questions in macroeconomics. Economists today routinely analyze systems in which agents operate in complex probabilistic environments to understand interactions about which the great theorists of an earlier generation could only speculate. This sea change is due primarily to Lucas. This essay is reprinted from the Journal of Economic Perspectives (Winter 1998, vol. 12, no. 1, pp. 171–86) with the permission of the American Economic Association.Economists