Multiplicities of compact lie group representations via Berezin quantization

Benjamin Cahen

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Stratonovich-Weyl correspondence for the Jacobi group

Benjamin Cahen (2014)

Communications in Mathematics

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We construct and study a Stratonovich-Weyl correspondence for the holomorphic representations of the Jacobi group.

Stratonovich-Weyl correspondence for discrete series representations

Benjamin Cahen (2011)

Archivum Mathematicum

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Let $M = G / K$ be a Hermitian symmetric space of the noncompact type and let $π$ be a discrete series representation of $G$ holomorphically induced from a unitary character of $K$ . Following an idea of Figueroa, Gracia-Bondìa and Vàrilly, we construct a Stratonovich-Weyl correspondence for the triple $(G, π, M)$ by a suitable modification of the Berezin calculus on $M$ . We extend the corresponding Berezin transform to a class of functions on $M$ which contains the Berezin symbol of $d π (X)$ for $X$ in the Lie algebra $𝔤$ of...

Quantum co-adjoint orbits of the group of affine transformations of the complex line.

Do Ngoc Diep, Nguyen Viet Hai (2001)

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A method for weight multiplicity computation based on Berezin quantization.

Bar-Moshe, David (2009)

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Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Mitsuo Morimoto, Keiko Fujita (1996)

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Let L(z) be the Lie norm on $\tilde{} = ℂ^{n + 1}$ and L*(z) the dual Lie norm. We denote by $_{Δ} (\tilde{B} (R))$ the space of complex harmonic functions on the open Lie ball $\tilde{B} (R)$ and by $E x p_{Δ} (\tilde{}; (A, L *))$ the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.

Weyl quantization for principal series.

Cahen, Benjamin (2007)

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On conditions for engineering stability of dynamical systems with variable structure.

Matvijchuk, K.S. (2000)

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