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Asymptotics of unitary matrix elements in canonical bases

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arxiv 2405.06137 v1 pith:QINGER2S submitted 2024-05-09 math.RT math-phmath.DGmath.MPmath.SG

Louis Ioos This is my paper · ORCID
classification math.RTmath-phmath.DGmath.MPmath.SG
keywords asymptoticselementsbasescanonicalmatrixrepresentationsunitaryassociated
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We compute the asymptotics of matrix elements in canonical bases of irreducible representations of the unitary group as the highest weight goes to infinity, in terms of the symplectic geometry of the associated coadjoint orbit. This uses tools of Berezin-Toeplitz quantization, and recovers as a special case the asymptotics of Wigner's d-matrix elements for the spin representations in quantum mechanics.

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  1. Optimal Remainder Estimates in the Quantization of Complex Projective Spaces

    math-ph 2025-08 conditional novelty 6.0 of 10

    Berezin-Toeplitz quantization on CP^{d-1} admits remainder bounds controlled by the next expansion term, with sharp constants and minimal regularity.

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