From Twisted Quantum Loop Algebras to Twisted Yangians

We prove how the Yangian of $\mathfrak{gl}_N$ in its RTT presentation and Olshanski's twisted Yangians for the orthogonal and symplectic Lie algebras can be obtained by a degeneration process from the corresponding quantum loop algebra and some of its twisted analogues

Double affine Lie algebras and finite groups

We introduce and begin to study Lie theoretical analogs of symplectic reflection algebras for a finite cyclic group, which we call "cyclic double affine Lie algebra". We focus on type A : in the finite (resp. affine, double affine) case, we prove that these structures are finite (resp. affine, toroidal) type Lie algebras, but the gradings differ. The case which is essentially new involves $\mathbb{C}[u,v]$. We describe its universal central extensions and start the study of its representation theory, in particular of its highest weight integrable modules and Weyl modules. We also consider the first Weyl algebra $A_1$ instead of the polynomial ring $\mathbb{C}[u,v]$, and, more generally, a rank one rational Cherednik algebra. We study quasi-finite highest weight representations of these Lie algebras.Comment: 31 page

The Response of Hours to a Technology Shock: a Two-Step Structural VAR Approach

The response of hours worked to a technology shock is an important and a controversial issue in macroeconomics. Unfortunately, the estimated response is generally sensitive to the specification of hours in SVARs. This paper uses a simple two-step approach in order to consistently estimate technology shocks from a SVAR model and the response of hours that follow this shock. The first step considers a SVAR model with a set of relevant stationary variables, but excluding hours. Given a consistent estimate of technology shocks in the first step, the response of hours to this shock is estimated in a second step. When applied to US data, the two-step approach predicts a short-run decrease of hours after a technology improvement followed by a hump-shaped positive response. This result is robust to the specification of hours, different sample periods, measures of hours and output and to the variables included in the VAR in the first step.SVARs, long-run restriction, technology shocks, consumption to output ratio, hours worked

Inflation Targeting and Q Volatility in Small Open Economies

This paper examines the welfare implications of managing Q with inflation targeting by monetary authorities who have to "learn" the laws of motion for both inflation and the rate of growth of Q. Our results show that the Central Bank can achieve great success in reducing the volatility of GDP growth with basically the same inflation volatility, if it incorporates this additional target into its policy regime. However, the welfare effects are generally lower, in terms of consumption, when the monetary authorithy reacts to Q growth as well as inflationTobin's Q, monetary policy, learning

Identification of Technology Shocks in Structural VARs

The usefulness of SVARs for developing empirically plausible models is actually subject to many controversies in quantitative macroeconomics. In this paper, we propose a simple alternative two step SVARs based procedure which consistently identifies and estimates the effect of permanent technology shocks on aggregate variables. Simulation experiments from a standard business cycle model show that our approach outperforms standard SVARs. The two step procedure, when applied to actual data, predicts a significant short-run decrease of hours after a technology improvement followed by a delayed and hump-shaped positive response. Additionally, the rate of inflation and the nominal interest rate displays a significant decrease after a positive technology shock.SVARs, long-run restriction, technology shocks, consumption to output ratio, hours worked

Vertex Representations for Yangians of Kac-Moody algebras

30 pagesUsing vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the PBW property for simply laced affine Yangians.Peer reviewe