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

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

Many-spinon states and the secret significance of Young tableaux

We establish a one-to-one correspondence between the Young tableaux classifying the total spin representations of N spins and the exact eigenstates of the the Haldane-Shastry model for a chain with N sites classified by the total spins and the fractionally spaced single-particle momenta of the spinons.Comment: 4 pages, 3 figure

Equivariant map superalgebras

Suppose a group $\Gamma$ acts on a scheme $X$ and a Lie superalgebra $\mathfrak{g}$. The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $X$ to $\mathfrak{g}$. We classify the irreducible finite dimensional modules for these superalgebras under the assumptions that the coordinate ring of $X$ is finitely generated, $\Gamma$ is finite abelian and acts freely on the rational points of $X$, and $\mathfrak{g}$ is a basic classical Lie superalgebra (or $\mathfrak{sl}(n,n)$, $n > 0$, if $\Gamma$ is trivial). We show that they are all (tensor products of) generalized evaluation modules and are parameterized by a certain set of equivariant finitely supported maps defined on $X$. Furthermore, in the case that the even part of $\mathfrak{g}$ is semisimple, we show that all such modules are in fact (tensor products of) evaluation modules. On the other hand, if the even part of $\mathfrak{g}$ is not semisimple (more generally, if $\mathfrak{g}$ is of type I), we introduce a natural generalization of Kac modules and show that all irreducible finite dimensional modules are quotients of these. As a special case, our results give the first classification of the irreducible finite dimensional modules for twisted loop superalgebras.Comment: 27 pages. v2: Section numbering changed to match published version. Other minor corrections. v3: Minor corrections (see change log at end of introduction

On minimal affinizations of representations of quantum groups

In this paper we study minimal affinizations of representations of quantum groups (generalizations of Kirillov-Reshetikhin modules of quantum affine algebras introduced by Chari). We prove that all minimal affinizations in types A, B, G are special in the sense of monomials. Although this property is not satisfied in general, we also prove an analog property for a large class of minimal affinization in types C, D, F. As an application, the Frenkel-Mukhin algorithm works for these modules. For minimal affinizations of type A, B we prove the thin property (the l-weight spaces are of dimension 1) and a conjecture of Nakai-Nakanishi (already known for type A). The proof of the special property is extended uniformly for more general quantum affinizations of quantum Kac-Moody algebras.Comment: 38 pages; references and additional results added. Accepted for publication in Communications in Mathematical Physic

Inflation, growth, and financial intermediation

Inflation (Finance)

The growth effects of monetary policy

This article investigates the relationship between inflation and output, in the data and in standard models. The article reports that empirical cross-country studies generally find a nonlinear, negative relationship between inflation and output, a relationship that standard models cannot come close to reproducing. The article demonstrates that the models' problem may be due to their standard narrow assumption that all money is held by the public for making transactions. When the models are adjusted to also assume that banks are required to hold money, the models do a much better job. The article concludes that researchers interested in studying the effects of monetary policy on growth should shift their attention away from printing money and toward the study of banking and financial regulations.Economic development ; Monetary policy

Extensions and block decompositions for finite-dimensional representations of equivariant map algebras

Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible finite-dimensional representations of these algebras were classified in previous work with P. Senesi, where it was shown that they are all tensor products of evaluation representations and one-dimensional representations. In the current paper, we describe the extensions between irreducible finite-dimensional representations of an equivariant map algebra in the case that $X$ is an affine scheme of finite type and $\mathfrak{g}$ is reductive. This allows us to also describe explicitly the blocks of the category of finite-dimensional representations in terms of spectral characters, whose definition we extend to this general setting. Applying our results to the case of generalized current algebras (the case where the group acting is trivial), we recover known results but with very different proofs. For (twisted) loop algebras, we recover known results on block decompositions (again with very different proofs) and new explicit formulas for extensions. Finally, specializing our results to the case of (twisted) multiloop algebras and generalized Onsager algebras yields previously unknown results on both extensions and block decompositions.Comment: 41 pages; v2: minor corrections, formatting changed to match published versio

Strategic delegation in monetary unions

In monetary unions, monetary policy is typically made by delegates of the member countries. This procedure raises the possibility of strategic delegation - that countries may choose the types of delegates to influence outcomes in their favor. We show that without commitment in monetary policy, strategic delegation arises if and only if three conditions are met: shocks affecting individual countries are not perfectly correlated, risk-sharing across countries is imperfect, and the Phillips Curve is nonlinear. Moreover, inflation rates are inefficiently high. We argue that ways of solving the commitment problem, including the emphasis on price stability in the agreements constituting the European Union are especially valuable when strategic delegation is a problem.Strategic delegation, monetary union, time-consistency, monetary policy

The economics of split-ticket voting in representative democracies

In U.S. elections, voters often vote for candidates from different parties for president and Congress. Voters also express dissatisfaction with the performance of Congress as a whole and satisfaction with their own representative. We develop a model of split-ticket voting in which government spending is financed by uniform taxes but the benefits from this spending are concentrated. While the model generates split-ticket voting, overall spending is too high only if the president’s powers are limited. Overall spending is too high in a parliamentary system, and our model can be used as the basis of an argument for term limits.Government spending policy