An explicit field-independent SL2-equivariant isomorphism is given between tensor invariant spaces and plethysm spaces, extending Hermite reciprocity and related maps, plus a combinatorial proof that the Hermite map is triangular with 1s on the diagonal.
Representation theory: a first course , volume 129
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Symmetry reduction makes the Berta et al. SDP hierarchy for quantum channel fidelity computable in time polynomial in hierarchy level and input dimension when output dimension is fixed.
Derives the spectral decomposition of word statistics with explicit eigenvectors and eigenvalues for the covariance matrix of subsequence counts in random texts.
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Field-independent Kronecker-plethysm isomorphisms
An explicit field-independent SL2-equivariant isomorphism is given between tensor invariant spaces and plethysm spaces, extending Hermite reciprocity and related maps, plus a combinatorial proof that the Hermite map is triangular with 1s on the diagonal.
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Efficient Approximation of Quantum Channel Fidelity Exploiting Symmetry
Symmetry reduction makes the Berta et al. SDP hierarchy for quantum channel fidelity computable in time polynomial in hierarchy level and input dimension when output dimension is fixed.
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Spectral Analysis of Word Statistics
Derives the spectral decomposition of word statistics with explicit eigenvectors and eigenvalues for the covariance matrix of subsequence counts in random texts.