One dimensional chiral Hubbard model reduces to the Haldane-Shastry spin chain at half-filling with large but finite on-site energy U . In this talk, we show that the Gutzwiller-Jastrow wavefunctions are the eigen-states of the Hubbard model at U = +∞ at less than half-filling. The full energy spectrum and an infinite set of mutually commuting constants of motion are also given in this limit fo...

Duality in the integrable systems arising in the context of Seiberg-Witten theory shows that their tau-functions indeed can be seen as generating functions for the mutually Poisson-commuting hamiltonians of the dual systems. We demonstrate that the Θ-function coefficients of their expansion can be expressed entirely in terms of the co-ordinates of the Seiberg-Witten integrable system, being, th...

This paper solves the two-sided version and provides a counterexample to general of 2003 conjecture by Hadwin Larson. Consider evaluations linear matrix pencils $L=T_0+x_1T_1+\cdots+x_mT_m$ on tuples as $L(X_1,\dots,X_m)=I\otimes T_0+X_1\otimes T_1+\cdots+X_m\otimes T_m$. It is shown that ranks constitute collection separating invariants for simultaneous similarity tuples. That is, $m$-tuples $...

We study a variety of modes (idempotent algebras with mutually commuting term operations), so called differential modes, having a strongly solvable chain 0 ≤ α ≤ 1 in their congruence lattices. We show an explicit description of subdirectly irreducible algebras in this variety, and use it to compute residual bounds of its subvarieties. It follows from our results that all subvarieties with a fi...

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

In this note, we show that quasi-free Hilbert modules R defined over natural function algebras satisfying a certain positivity condition, defined via the hereditary functional calculus, admit a dilation (actually a co-extension) to the Hardy module over the polydisk. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. Some consequence...

An r-graph is a graph whose basic elements are its vertices and r-tuples . It is proved that to every 1 and r there is an e(l, r) so that for n > no every r-graph of n vertices and n'-E(i, r) r-tuples contains r . /vertices P),I5 j < r, l < i < l, so that all the r-tuples (x i ,( 1 ), xi2 (2 ) ' . . . , x1 (')) occur in the r-graph . By an r-graph G (')(r >_ 2) we shall mean a graph whose basic...

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W -orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representations of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A ...

We examine a two-parameter (, λ) deformation of the Poincarè algebra which is covariant under the action of SLq(2, C). When λ → 0 it yields the Poincarè algebra, while in the → 0 limit we recover the classical quadratic algebra discussed previously in [1], [2]. The analogues of the Pauli-Lubanski vector w and Casimirs p 2 and w 2 are found and a set of mutually commuting operators is constructed.

Based on a novel point of view on 1-dimensional Gaussian quadrature, we present a new approach to the computation of d-dimensional cubature formulae. It is well known that the nodes of 1-dimensional Gaussian quadrature can be computed as eigenvalues of the so-called Jacobi matrix. The d-dimensional analog is that cubature nodes can be obtained from the eigenvalues of certain mutually commuting ...