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pro vyhledávání: '"Coquereaux, Robert"'
Autor:
Coquereaux, Robert
Publikováno v:
In: Flandrin, P., Jaffard, S., Paul, T., Torresani, B. (eds) Theoretical Physics, Wavelets, Analysis, Genomics. An Indisciplinary Tribute to Alex Grossmann. Applied and Numerical Harmonic Analysis. Birkh\"auser, Cham. 2023
After recalling the notion of higher roots (or hyper-roots) associated with "quantum modules" of type $(G, k)$, for $G$ a semi-simple Lie group and $k$ a positive integer, following the definition given by A. Ocneanu in 2000, we study the theta serie
Externí odkaz:
http://arxiv.org/abs/2409.02926
Publikováno v:
Journal of Integer Sequences, Vol. 27 (2024), Article 24.2.6
We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent Bell, Stirling numbers, and Fa\`a di Bruno coefficients. Besides attempting to summarize what is already know
Externí odkaz:
http://arxiv.org/abs/2305.01100
Autor:
Coquereaux, Robert
Publikováno v:
J. Math. Phys. 64, 031703 (2023)
These notes contain essentially a rewriting of several properties of two well-known quantities, the so-called theta symbol (or triangular symbol), which is rational, and the 6j symbol, which is usually irrational, in terms of two related integer-valu
Externí odkaz:
http://arxiv.org/abs/2209.15247
Autor:
Coquereaux, Robert
This is a collection of notes on the properties of left-invariant metrics on the eight-dimensional compact Lie group SU(3). Among other topics we investigate the existence of invariant pseudo-Riemannian Einstein metrics on this manifold. We recover t
Externí odkaz:
http://arxiv.org/abs/2107.12285
Autor:
Coquereaux, Robert
Publikováno v:
Phys. Part. Nuclei Lett. 17, 763-773 (2020)
The present contribution is the written counterpart of a talk given in Yerevan at the SQS'2019 International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2019, 26 August - August 31, 2019). After a short presentation of various pictographs
Externí odkaz:
http://arxiv.org/abs/2003.00358
We reconsider the two related problems: distribution of the diagonal elements of a Hermitian n x n matrix of known eigenvalues (Schur) and determination of multiplicities of weights in a given irreducible representation of SU(n) (Kostka). It is well
Externí odkaz:
http://arxiv.org/abs/2001.08046
Publikováno v:
J. Stat. Mech. (2019) 094018, Special Issue in Memory of Vladimir Rittenberg
We review recent progress on Horn's problem, which asks for a description of the possible eigenspectra of the sum of two matrices with known eigenvalues. After revisiting the classical case, we consider several generalizations in which the space of m
Externí odkaz:
http://arxiv.org/abs/1905.09662
We consider an extended version of Horn's problem: given two orbits $\mathcal{O}_\alpha$ and $\mathcal{O}_\beta$ of a linear representation of a compact Lie group, let $A\in \mathcal{O}_\alpha$, $B\in \mathcal{O}_\beta$ be independent and invariantly
Externí odkaz:
http://arxiv.org/abs/1904.00752
Publikováno v:
SIGMA 15 (2019), 029, 34 pages
Horn's problem, i.e., the study of the eigenvalues of the sum $C=A+B$ of two matrices, given the spectrum of $A$ and of $B$, is re-examined, comparing the case of real symmetric, complex Hermitian and self-dual quaternionic $3\times 3$ matrices. In p
Externí odkaz:
http://arxiv.org/abs/1809.03394
Autor:
Coquereaux, Robert
Publikováno v:
Experimental Mathematics, April 2, 2018
We recall the definition of the hyper-roots that can be associated to modules-categories over the fusion categories defined by the choice of a simple Lie group G together with a positive integer k. This definition was proposed in 2000, using another
Externí odkaz:
http://arxiv.org/abs/1708.00560