Irreducible factors of modular representations of mapping class groups arising in Integral TQFT

We find decomposition series of length at most two for modular representations in positive characteristic of mapping class groups of surfaces induced by an integral version of the Witten-Reshetikhin-Turaev SO(3)-TQFT at the p-th root of unity, where p is an odd prime. The dimensions of the irreducible factors are given by Verlinde-type formulas.Comment: 29 pages, two conjectures made in Remark 7.3 of version 1 are now proved in the added subsection 7.5; simplified equation (5); added Remark 7.5; rewrote parts of section 4 to make paper more self-containe

An application of TQFT to modular representation theory

For p>3 a prime, and g>2 an integer, we use Topological Quantum Field Theory (TQFT) to study a family of p-1 highest weight modules L_p(lambda) for the symplectic group Sp(2g,K) where K is an algebraically closed field of characteristic p. This permits explicit formulae for the dimension and the formal character of L_p(lambda) for these highest weights.Comment: 24 pages, 3 figures. v2: Lemma 3.1 and Appendix A adde

Integral Lattices in TQFT

We find explicit bases for naturally defined lattices over a ring of algebraic integers in the SO(3) TQFT-modules of surfaces at roots of unity of odd prime order. Some applications relating quantum invariants to classical 3-manifold topology are given.Comment: 31 pages, v2: minor modifications. To appear in Ann. Sci. Ecole Norm. Su

Integral bases for TQFT modules and unimodular representations of mapping class groups

We construct integral bases for the SO(3)-TQFT-modules of surfaces in genus one and two at roots of unity of prime order and show that the corresponding mapping class group representations preserve a unimodular Hermitian form over a ring of algebraic integers. For higher genus surfaces the Hermitian form sometimes must be non-unimodular. In one such case, genus 3 and p=5, we still give an explicit basis

Great Moderation(s) and U.S. Interest Rates: Unconditional Evidence

The US economy experienced a Great Moderation sometime in the mid-1980s -- a fall in the volatility of output growth -- at the same time as a fall in both the volatility of inflation and the average rate of inflation. We put this moderation in historical perspective by comparing it to the post-WWII moderation. According to theory, the statistical moments -- both real and nominal -- that shift during these moderations in turn influence interest rates. We examine the predictions for shifts in the unconditional average of US interest rates. A central finding is that such shifts probably were due to changes in average inflation rather than to those in the variances of inflation and consumption growth.great moderation, asset pricing

Identifying the New Keynesian Phillips curve

Phillips curves are central to discussions of inflation dynamics and monetary policy. New Keynesian Phillips curves describe how past inflation, expected future inflation, and a measure of real marginal cost or an output gap drive the current inflation rate. This paper studies the (potential) weak identification of these curves under generalized methods of moments (GMM) and traces this syndrome to a lack of persistence in either exogenous variables or shocks. The authors employ analytic methods to understand the identification problem in several statistical environments: under strict exogeneity, in a vector autoregression, and in the canonical three-equation, New Keynesian model. Given U.S., U.K., and Canadian data, they revisit the empirical evidence and construct tests and confidence intervals based on exact and pivotal Anderson-Rubin statistics that are robust to weak identification. These tests find little evidence of forward-looking inflation dynamics.

Identifying the New Keynesian Phillips Curve

Phillips curves are central to discussions of inflation dynamics and monetary policy. New Keynesian Phillips curves describe how past inflation, expected future inflation, and a measure of real marginal cost or an output gap drive the current inflation rate. This paper studies the (potential) weak identification of these curves under GMM and traces this syndrome to a lack of persistence in either exogenous variables or shocks. We employ analytic methods to understand the identification problem in several statistical environments: under strict exogeneity, in a vector autoregression, and in the canonical three-equation, New Keynesian model. Given U.S., U.K., and Canadian data, we revisit the empirical evidence and construct tests and confidence intervals based on exact and pivotal Anderson-Rubin statistics that are robust to weak identification. These tests find little evidence of forward-looking inflation dynamics.Phillips curve, Keynesian, identification, inflation