Note on 'N-pseudoreductions' of the KP hierarchy

The group-theoretical side of N-pseudoreductions is discussed. The resulting equations are shown to be easy transformations of the N-KdV hierarch

Defining relations for Lie algebras of vector fields

AbstractWe calculated defining relations of the graded nilpotent positive part of Lie algebras of vector fields. These calculations suggest that for Wn,ln and Kn (n sufficiently large) there are only tri relations, i.e. relations of degree 2. ForHn however, we prove that there are non-trivial relations of degree 3, which form a standard module

Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere

We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials

Loss aversion with a state-dependent reference point

This study investigates loss aversion when the reference point is a state-dependent random variable. This case describes, for example, a money manager being evaluated relative to a risky benchmark index rather than a fixed target return level. Using a state-dependent structure, prospects are more (less) attractive if they depend positively (negatively) on the reference point. In addition, the structure avoids an inherent aversion to risky prospects and yields no losses when the prospect and the reference point are the same. Related to this, the optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) when the reference point is selected completely endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. For example, the typical investment benchmark index is externally fixed by the investment principal for the duration of the investment mandate. We develop a choice model where adjustment costs cause stickiness relative to an initial exogenous reference point.Reference-dependent preferences, stochastic reference point, loss aversion, disappointment theory, regret theory.

Infinite families of superintegrable systems separable in subgroup coordinates

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure