Affiliation: Physics Department, Laval University
Email: pmathieu@phy.ulaval.ca
Title Of Talk: New partitions form physics
Abstract: I describe two new types of partitions that have popped up recently in physical problems. The first one corresponds to pseudo-partitions that have been dubbed `jagged partitions', in which the usual non-increasing condition on parts $n_i\geq $n_{i+1}$ has been replaced by the weaker requirement $n_i \geq n_{i+1}-1$ and $n_i \geq n_{i+2}$. In the two distinct physical contexts in which they appear (particular classes of conformal field theories), they are further subject to special conditions at distance $K-1$, where the parameter $K$ is either even or odd according to the type of models considered. The generating function that counts such restricted jagged partitions is related to multi-sums first introduced by Bressoud. Supersymmetric quantum many-body problems of the Calogero-Moser-Sutehrland-type are at the origins of the second new type of partitions. These models lead to supersymmetric extensions of the defining eigenvalue problem for the Jack polynomials. They involve both commuting and anticommuting variables. The resulting eigenfunctions, called Jack superpolynomials, are labeled by superpartitions. A superpartition is the juxtaposition of two partitions, one of which being composed of distinct parts. The concept of superpartitions is the cornerstone of the emerging theory of symmetric superpolynomials.
Last update made Tue Nov 16 16:23:04 EST 2004.
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