Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type

We introduce and study natural generalisations of the Hermite and Laguerre polynomials in the ring of symmetric functions as eigenfunctions of infinite-dimensional analogues of partial differential operators of Calogero-Moser-Sutherland (CMS) type. In particular, we obtain generating functions, duality relations, limit transitions from Jacobi symmetric functions, and Pieri formulae, as well as the integrability of the corresponding operators. We also determine all ideals in the ring of symmetric functions that are spanned by either Hermite or Laguerre symmetric functions, and by restriction of the corresponding infinite-dimensional CMS operators onto quotient rings given by such ideals we obtain so-called deformed CMS operators. As a consequence of this restriction procedure, we deduce, in particular, infinite sets of polynomial eigenfunctions, which we shall refer to as super Hermite and super Laguerre polynomials, as well as the integrability, of these deformed CMS operators. We also introduce and study series of a generalised hypergeometric type, in the context of both symmetric functions and 'super' polynomials

Jack superpolynomials: physical and combinatorial definitions

Jack superpolynomials are eigenfunctions of the supersymmetric extension of the quantum trigonometric Calogero-Moser-Sutherland. They are orthogonal with respect to the scalar product, dubbed physical, that is naturally induced by this quantum-mechanical problem. But Jack superpolynomials can also be defined more combinatorially, starting from the multiplicative bases of symmetric superpolynomials, enforcing orthogonality with respect to a one-parameter deformation of the combinatorial scalar product. Both constructions turns out to be equivalent. This provides strong support for the correctness of the various underlying constructions and for the pivotal role of Jack superpolynomials in the theory of symmetric superpolynomials.Comment: 6 pages. To appear in the proceedings of the {\it XIII International Colloquium on Integrable Systems and Quantum Groups}, Czech. J . Phys., June 17-19 2004, Doppler Institute, Czech Technical Universit

The effect of deglacial meltwater processes on kimberlite indicator mineral concentrations in glacial sediments

Successful diamond exploration projects in glaciated terrain depend on effective drift prospecting methods. This thesis assesses the effects of deglacial meltwater on kimberlite indicator mineral contents in subglacial meltwater corridor sediments. Located 100 km west of Lac de Gras, NWT, the study area has diamond potential and contains subglacial meltwater corridors and unmodified till. A 1:15 000 surficial geology map was produced. Meltwater corridors bisect areas of till veneer and blanket and contain glaciofluvial deposits including eskers and glaciofluvial hummocks. These hummocks form by subglacial meltwater erosion of till and rapid deposition. Till has more silt and clay than meltwater-affected sediments; this affects normalization of analytical results with glaciofluvial hummocks containing higher counts of pyropes. Identification of subglacial meltwater corridor sediments including glaciofluvial hummocks is crucial as they have different compositions and transport histories than till. These differences must be considered when interpreting surficial exploration datasets and planning sampling programs