Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $α$

Details Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $α$ Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $α$

2007-11-20

arxiv.org/abs/0711.3062v2

Phys. Rev. B 77, 184502 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages

Scientific paper

10.1103/PhysRevB.77.184502

We present several conjectures on the behavior and clustering properties of Jack polynomials at \emph{negative} parameter $\alpha=-\frac{k+1}{r-1}$, of partitions that violate the $(k,r,N)$ admissibility rule of Feigin \emph{et. al.} [\onlinecite{feigin2002}]. We find that "highest weight" Jack polynomials of specific partitions represent the minimum degree polynomials in $N$ variables that vanish when $s$ distinct clusters of $k+1$ particles are formed, with $s$ and $k$ positive integers. Explicit counting formulas are conjectured. The generalized clustering conditions are useful in a forthcoming description of fractional quantum Hall quasiparticles.

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