Generalized clustering conditions of Jack polynomials at negative Jack parameterα

B. Andrei Bernevig, F. D. M. Haldane
2008 Physical Review B  
We present several conjectures on the behavior and clustering properties of Jack polynomials at negative parameter α=-k+1/r-1, of partitions that violate the (k,r,N) admissibility rule of Feigin et. al. [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
more » ... clustering conditions are useful in a forthcoming description of fractional quantum Hall quasiparticles.
doi:10.1103/physrevb.77.184502 fatcat:6ahhmkszxbh6jbucmce36y5ksa