Eddy Ardonne et al 2005 J. Phys. A: Math. Gen. 38 617 doi:10.1088/0305-4470/38/3/006
Filling the Bose sea: symmetric quantum Hall edge states and affine characters
Eddy Ardonne1, Rinat Kedem2 and Michael Stone1
Show affiliationsWe 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 
. 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 
edge-current algebra. We also show that a spin-singlet, two-component k-clustered boson fluid is similarly related to integrable representations of 
. Parafermions are not necessary for these constructions.
- PACS
- MSC
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17B65 Infinite-dimensional Lie (super)algebras (See also 22E65)
- Subjects
- Dates
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Issue 3 (21 January 2005)
Received 23 September 2004, in final form 12 November 2004
Published 23 December 2004
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Filling the Bose sea: symmetric quantum Hall edge states and affine characters
Eddy Ardonne et al 2005 J. Phys. A: Math. Gen. 38 617
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