2008/10/06 by Adrien Boussicault, A Boussicault, Jean-Gabriel Luque +3 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Canonical normal form #Computation #Decomposition #Expression (computer science) #Function (biology) #Mathematical functions and polynomials #Square (algebra) #Tensor decomposition and applications #Vandermonde matrix #Wave function #math-ph #math.CO #math.MP #msc:05E05 #msc:15A69 #msc:81-08 #msc:81V70
paper · pdf · doi:10.1088/1751-8113/42/14/145301
published in Journal of Physics A Mathematical and Theoretical 42(14), 145301 (Institute of Physics)
arxiv created 2008/10/06 · openalex publication_date 2009/03/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The decomposition of the Laughlin wavefunction 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 this result to construct an algorithm allowing us to compute one coefficient of the development without computing the others. Thanks to a program in C , we performed the calculation for the square of the Vandermonde up to an alphabet of 11 letters.