Vertex--IRF correspondence and factorized L-operators for an elliptic R-operator

As for an elliptic $R$-operator which satisfies the Yang--Baxter equation, the incoming and outgoing intertwining vectors are constructed, and the vertex--IRF correspondence for the elliptic $R$-operator is obtained. The vertex--IRF correspondence implies that the Boltzmann weights of the IRF model satisfy the star--triangle relation. By means of these intertwining vectors, the factorized L-operators for the elliptic $R$-operator are also constructed. The vertex--IRF correspondence and the factorized L-operators for Belavin's $R$-matrix are reproduced from those of the elliptic $R$-operator.Comment: 25 pages, amslatex, no figure

ZnZ_n elliptic Gaudin model with open boundaries

The $Z_n$ elliptic Gaudin model with integrable boundaries specified by generic non-diagonal K-matrices with $n+1$ free boundary parameters is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained.Comment: 21 pages, Latex fil

Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the pp-Adics-Quantum Group Connection

We establish a previously conjectured connection between $p$-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which ``interpolate'' between the zonal spherical functions of related real and $p$\--adic symmetric spaces. The elliptic quantum algebras underlie the $Z_n$\--Baxter models. We show that in the n \air \infty limit, the Jost function for the scattering of {\em first} level excitations in the $Z_n$\--Baxter model coincides with the Harish\--Chandra\--like $c$\--function constructed from the Macdonald polynomials associated to the root system $A_1$. The partition function of the $Z_2$\--Baxter model itself is also expressed in terms of this Macdonald\--Harish\--Chandra\ $c$\--function, albeit in a less simple way. We relate the two parameters $q$ and $t$ of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular the $p$\--adic ``regimes'' in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of ``$q$\--deforming'' Euler products.Comment: 25 page

Do financial crises discipline future credit growth?

Purpose: The purpose of this paper is to test whether financial crises themselves provide some degree of ex post discipline. In other words, is there learning from the mistakes associated with crises? The authors test this hypothesis on credit growth, a frequent contributor to banking crises. Design/methodology/approach: The study uses statistical tests (comparison of means) on a sample of 72 banking crises, the onset of which occurred between 1980 and 2008. Tests for significance of the difference are conducted using Kolmogorov–Smirnov equality in distribution tests. Findings: The results show that real credit growth fell substantially (relative to average) by about 8 per cent points from pre- to post-crisis periods, and that average banking regulation and supervision strengthens after a crisis. Originality/value: This paper provides empirical support for the proposition that while financial markets may fail to give sufficient warning signals before a financial crisis, they may discipline governments to undertake reforms in the aftermath of a crisis