Strongly primitive species with potentials I: Mutations

Motivated by the mutation theory of quivers with potentials developed by Derksen-Weyman-Zelevinsky, and the representation-theoretic approach to cluster algebras it provides, we propose a mutation theory of species with potentials for species that arise from skew-symmetrizable matrices that admit a skew-symmetrizer with pairwise coprime diagonal entries. The class of skew-symmetrizable matrices covered by the mutation theory proposed here contains a class of matrices that do not admit global unfoldings, that is, unfoldings compatible with all possible sequences of mutations.Comment: 51 page

A Normal Country

During the 1990s, Russia underwent an extraordinary transformation from a communist dictatorship to a multi-party democracy, from a centrally planned economy to a market economy, and from a belligerent adversary of the West to a cooperative partner. Yet a consensus in the US circa 2000 viewed Russia as a disastrous and threatening failure, and the 1990s as a decade of catastrophe for its citizens. Analyzing a variety of economic and political data, we demonstrate a large gap between this perception and the facts. In contrast to the common image, by the late 1990s Russia had become a typical middle- income capitalist democracy.

Investor Protection and Equity Markets

We present a simple model of an entrepreneur going public in an environment with poor legal protection of outside shareholders. The model incorporates elements of Becker's (1968) crime and punishment' framework into a corporate finance environment of Jensen and Meckling (1976). We examine the entrepreneur's decision and the market equilibrium. The model is consistent with a number of empirical regularities concerning the relationship between investor protection and corporate finance.

Spin-Flavor Separation and Non-Fermi Liquid Behavior in the Multichannel Kondo Problem: A Large N Approach

We consider a $SU(N)\times SU(M)$ generalization of the multichannel single-impurity Kondo model which we solve analytically in the limit $N\rightarrow \infty$, $M\rightarrow\infty$, with $\gamma=M/N$ fixed. Non-Fermi liquid behavior of the single electron Green function and of the local spin and flavor susceptibilities occurs in both regimes, $N\le M$ and $N > M$, with leading critical exponents {\em identical} to those found in the conformal field theory solution for {\em all} $N$ and $M$ (with $M\ge 2$). We explain this remarkable agreement and connect it to ``spin-flavor separation", the essential feature of the non-Fermi-liquid fixed point of the multichannel Kondo problem.Comment: 14 pages, 1 Figure (Poscript file attached), Revte

Physical picture of the gapped excitation spectrum of the one-dimensional Hubbard model

A simple picture for the spectrum of the one-dimensional Hubbard model is presented using a classification of the eigenstates based on an intuitive bound-state Bethe-Ansatz approach. This approach allows us to prove a "string hypothesis" for complex momenta and derive an exact formulation of the Bethe-Ansatz equations including all states. Among other things we show that all gapped eigenstates have the Bethe-Ansatz form, contrary to assertions in the literature. The simplest excitations in the upper Hubbard band are computed: we find an unusual dispersion close to half-filling.Comment: 22 pages, revtex, 4 eps-figure

The Unofficial Economy in Transition

macroeconomics, official economy, public finances, economic growth