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 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

The New Keynesian Phillips curve : lessons from single-equation econometric estimation

We review single-equation methods for estimating the hybrid New Keynesian Phillips curve (NKPC) and then apply those methods to U.S. quarterly data for 1955?2007. Estimating the hybrid NKPC by the generalized method of moments yields stable coefficients with a large role for expected future inflation. Measures of marginal costs better explain U.S. inflation than does a range of measures of the output gap. But estimates of the slope of the NKPC are imprecise and confidence intervals that are robust to weak identification are wide. Further research on measuring marginal costs may reconcile these mixed findings. A reconciliation is important if the NKPC is to remain a fundamental component of models of the monetary transmission mechanism.Inflation (Finance) ; Phillips curve

Great moderations and U.S. interest rates: unconditional evidence

The Great Moderation refers to the fall in U.S. output growth volatility in the mid-1980s. At the same time, the United States experienced a moderation in inflation and lower average inflation. Using annual data since 1890, we find that an earlier, 1946 moderation in output and consumption growth was comparable to that of 1984. Using quarterly data since 1947, we also isolate the 1969–83 Great Inflation to refine the asset pricing implications of the moderations. Asset pricing theory predicts that moderations—real or nominal—influence interest rates. We examine the quantitative predictions of a consumption-based asset pricing model for shifts in the unconditional average of U.S. interest rates. A central finding is that such shifts probably were related to changes in average inflation rather than to moderations in inflation and consumption growth.Interest rates ; Inflation (Finance)

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

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

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