Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1843820 | Nuclear Physics B | 2011 | 20 Pages |
Abstract
In the study of fractional quantum Hall states, a certain clustering condition involving up to four integers has been identified. We give a simple proof that particular Jack polynomials with α=−(r−1)/(k+1)α=−(r−1)/(k+1), (r−1)(r−1) and (k+1)(k+1) relatively prime, and with partition given in terms of its frequencies by [n00(r−1)sk0r−1k0r−1k⋯0r−1m][n00(r−1)sk0r−1k0r−1k⋯0r−1m] satisfy this clustering condition. Our proof makes essential use of the fact that these Jack polynomials are translationally invariant. We also consider nonsymmetric Jack polynomials, symmetric and nonsymmetric generalized Hermite and Laguerre polynomials, and Macdonald polynomials from the viewpoint of the clustering.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Wendy Baratta, Peter J. Forrester,