### Abstract

We explore the structure of the bosonic analogues of the k-clustered 'parafermion' quantum Hall states. We show how the many-boson wavefunctions of k-clustered quantum Hall droplets appear naturally as matrix elements of ladder operators in integrable representations of the affine Lie algebra su(2) _{k}. Using results of Feigin and Stoyanovsky, we count the dimensions of spaces of symmetric polynomials with given k-clustering properties and show that as the droplet size grows the partition function of its edge excitations evolves into the character of the representation. This confirms that the Hilbert space of edge states coincides with the representation space of the su(2)_{k} edge-current algebra. We also show that a spin-singlet, two-component k-clustered boson fluid is similarly related to integrable representations of su(3). Parafermions are not necessary for these constructions.

Original language | English (US) |
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Pages (from-to) | 617-636 |

Number of pages | 20 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 38 |

Issue number | 3 |

DOIs | |

State | Published - Jan 21 2005 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

**Filling the Bose sea : Symmetric quantum Hall edge states and affine characters.** / Ardonne, Eddy; Kedem, Rinat; Stone, Michael.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 38, no. 3, pp. 617-636. https://doi.org/10.1088/0305-4470/38/3/006

}

TY - JOUR

T1 - Filling the Bose sea

T2 - Symmetric quantum Hall edge states and affine characters

AU - Ardonne, Eddy

AU - Kedem, Rinat

AU - Stone, Michael

PY - 2005/1/21

Y1 - 2005/1/21

N2 - We explore the structure of the bosonic analogues of the k-clustered 'parafermion' quantum Hall states. We show how the many-boson wavefunctions of k-clustered quantum Hall droplets appear naturally as matrix elements of ladder operators in integrable representations of the affine Lie algebra su(2) k. Using results of Feigin and Stoyanovsky, we count the dimensions of spaces of symmetric polynomials with given k-clustering properties and show that as the droplet size grows the partition function of its edge excitations evolves into the character of the representation. This confirms that the Hilbert space of edge states coincides with the representation space of the su(2)k edge-current algebra. We also show that a spin-singlet, two-component k-clustered boson fluid is similarly related to integrable representations of su(3). Parafermions are not necessary for these constructions.

AB - We explore the structure of the bosonic analogues of the k-clustered 'parafermion' quantum Hall states. We show how the many-boson wavefunctions of k-clustered quantum Hall droplets appear naturally as matrix elements of ladder operators in integrable representations of the affine Lie algebra su(2) k. Using results of Feigin and Stoyanovsky, we count the dimensions of spaces of symmetric polynomials with given k-clustering properties and show that as the droplet size grows the partition function of its edge excitations evolves into the character of the representation. This confirms that the Hilbert space of edge states coincides with the representation space of the su(2)k edge-current algebra. We also show that a spin-singlet, two-component k-clustered boson fluid is similarly related to integrable representations of su(3). Parafermions are not necessary for these constructions.

UR - http://www.scopus.com/inward/record.url?scp=12844261175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12844261175&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/38/3/006

DO - 10.1088/0305-4470/38/3/006

M3 - Article

AN - SCOPUS:12844261175

VL - 38

SP - 617

EP - 636

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 3

ER -