ar X iv : s ol v - in t / 9 61 00 06 v 1 9 O ct 1 99 6 ON THE SOLUTION OF NORMALITY EQUATIONS

ar X iv : s ol v - in t / 9 61 00 10 v 1 2 8 O ct 1 99 6 An orthogonal basis for the B N - type Calogero model

We investigate algebraic structure for the BN -type Calogero model by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provides an orthogonal basis.

ar X iv : s ol v - in t / 9 70 30 03 v 1 6 M ar 1 99 7 ON THE POINT TRANSFORMATIONS FOR THE SECOND ORDER DIFFERENTIAL EQUATIONS

Point transformations for the ordinary differential equations of the form y ′′ = P (x, y) + 3 Q(x, y) y ′ + 3 R(x, y) (y ′) 2 + S(x, y) (y ′) 3 are considered. Some classical results are resumed. Solution for the equivalence problem for the equations of general position is described.

ar X iv : s ol v - in t / 9 71 00 04 v 1 7 O ct 1 99 7 México ICN - UNAM 97 - 12 Two - body

Two Lie algebraic forms of the 2-body Elliptic Calogero model are presented. Translation-invariant and dilatation-invariant discretizations of the model are obtained.

ar X iv : s ol v - in t / 9 61 20 02 v 1 4 D ec 1 99 6 Correlators of the phase model

We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the " darkness formation probability " are calculated in the thermodynamical limit. These results can be used to construct integrable equations for the correlation functions and to calculate their asymptotics.

ar X iv : s ol v - in t / 9 70 80 06 v 1 1 4 A ug 1 99 7 Introduction to the Hirota bilinear method