2009
DOI: 10.1088/1751-8113/42/14/145301
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Hyperdeterminantal computation for the Laughlin wavefunction

Abstract: The decomposition of the Laughlin wave function in the Slater orthogonal basis appears in the discussion on the second-quantized form of the Laughlin states and is straightforwardly equivalent to the decomposition of the even powers of the Vandermonde determinants in the Schur basis. Such a computation is notoriously difficult and the coefficients of the expansion have not yet been interpreted. In our paper, we give an expression of these coefficients in terms of hyperdeterminants of sparse tensors. We use thi… Show more

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Cited by 6 publications
(13 citation statements)
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References 27 publications
(45 reference statements)
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“…. , 1), we note that (22) perfectly matches the value for the average of the determinant for a Jacobi ensemble with γ = 1, as computed from the Selberg integral (5):…”
Section: Hyperdeterminant Formula For Statistics Of Permanents Fosupporting
confidence: 77%
“…. , 1), we note that (22) perfectly matches the value for the average of the determinant for a Jacobi ensemble with γ = 1, as computed from the Selberg integral (5):…”
Section: Hyperdeterminant Formula For Statistics Of Permanents Fosupporting
confidence: 77%
“…The study of ϕ m L as a symmetric function generated literature for the purpose of the expansion in the Schur basis and the monomial basis [10,33]. This first case is particularly interesting because it is also related to rectangular Jack polynomials and hyperdeterminants [2,6,26]. Notice that, even in this (simplest) case, Macdonald polynomial provides a more regular framework for the study of these functions.…”
Section: The Quasistaircase Partitionmentioning
confidence: 99%
“…, z τ l . Moreover, this identity is thus invariant under any permutation of these variables, and so h S (x(Y)s i ) = 0 in (6).…”
mentioning
confidence: 99%
See 1 more Smart Citation
“…Date: August 8, 2018. However, a combinatorial interpretation for the coefficient of a given Schur function is still unknown. Recently, Boussicault, Luque and Tollu [2] provided a purely numerical algorithm for computing the coefficient of a given Schur function in the decomposition without computing the other coefficients. The algorithm uses hyperdeterminants and their Laplace expansion.…”
Section: Introductionmentioning
confidence: 99%