A. P. Isaev, A. A. Provorov, “Projectors on invariant subspaces of representations $\operatorname{ad}^{\otimes2}$ of Lie algebras $so(N)$ and $sp(2r)$ and Vogel parameterization”, TMF, 206:1 (2021), 3–22; Theoret. and Math. Phys., 206:1 (2021), 1

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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 206, Number 1, Pages 3–22
DOI: https://doi.org/10.4213/tmf9984 (Mi tmf9984)

This article is cited in 9 scientific papers (total in 9 papers)

Projectors on invariant subspaces of representations

{ad}^{\otimes 2}

$\operatorname{ad}^{\otimes2}$ of Lie algebras

$so(N)$ and

$sp(2r)$ and Vogel parameterization

A. P. Isaev^ab, A. A. Provorov^ac

^a Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
^b Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
^c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Oblast, Russia

Full-text PDF (585 kB) Citations (9)

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DOI: https://doi.org/10.4213/tmf9984

Abstract: Using the split Casimir operator, we find explicit formulas for the projectors onto invariant subspaces of the

$\operatorname{ad}^{\otimes2}$ representation of the algebras

$so(N)$ and

$sp(2r)$ . We also consider these projectors from the standpoint of the universal description of complex simple Lie algebras using the Vogel parameterization.

Keywords: invariant subspace, projector, simple Lie algebra, split Casimir operator, Vogel parameter.

Funding agency	Grant number
Russian Foundation for Basic Research	20-52-12003\20 19-01-00726
The research of A. P. Isaev was supported by the Russian Foundation for Basic Research (Grant No. 19-01-00726). The research of A. A. Provorov was supported by the Russian Foundation for Basic Research (Grant No. 20-52-12003 $\backslash$ 20).

Received: 15.09.2020
Revised: 15.09.2020

English version:
Theoretical and Mathematical Physics, 2021, Volume 206, Issue 1, Pages 1–18
DOI: https://doi.org/10.1134/S0040577921010013

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. P. Isaev, A. A. Provorov, “Projectors on invariant subspaces of representations

$\operatorname{ad}^{\otimes2}$ of Lie algebras

$so(N)$ and

$sp(2r)$ and Vogel parameterization”, TMF, 206:1 (2021), 3–22; Theoret. and Math. Phys., 206:1 (2021), 1–18

Citation in format AMSBIB

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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2021TMP...206....1I}

\transl

\jour Theoret. and Math. Phys.

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\crossref{https://doi.org/10.1134/S0040577921010013}

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Linking options:

https://www.mathnet.ru/eng/tmf9984

https://doi.org/10.4213/tmf9984

https://www.mathnet.ru/eng/tmf/v206/i1/p3

This publication is cited in the following 9 articles:

A. P. Isaev, S. O. Krivonos, “The split $5$-Casimir operator and the structure of $\wedge \mathfrak{ad}^{\otimes 5}$”, Izv. Math., 89:1 (2025), 15–25
Vladimir K. Dobrev, “Canonical Construction of Invariant Differential Operators: A Review”, Symmetry, 16:2 (2024), 151
M. Avetisyan, A.P. Isaev, S.O. Krivonos, R. Mkrtchyan, “The Uniform Structure of $\mathfrak{g}^{\otimes 4}$”, Russ. J. Math. Phys., 31:3 (2024), 379
Yu-tin Huang, Hynek Paul, Michele Santagata, “Non-analytic terms of string amplitudes from partial waves”, J. High Energ. Phys., 2024:11 (2024)
H. Paul, M. Santagata, “Genus-one open string amplitudes on $\mathrm{AdS_5\times S^3}$ from CFT”, J. High Energ. Phys., 2023:12 (2023), 57
S. M. Chester, “Bootstrapping $4d$ $\mathcal{N} = 2$ gauge theories: the case of SQCD”, J. High Energ. Phys., 2023:1 (2023), 107
A. P. Isaev, A. A. Provorov, “Split Casimir operator and solutions of the Yang–Baxter equation for the $osp(M|N)$ and $s\ell(M|N)$ Lie superalgebras, higher Casimir operators, and the Vogel parameters”, Theoret. and Math. Phys., 210:2 (2022), 224–260
Isaev A.P., Krivonos S.O., “Split Casimir Operator For Simple Lie Algebras, Solutions of Yang-Baxter Equations, and Vogel Parameters”, J. Math. Phys., 62:8 (2021), 083503
Alexey Isaev, Sergey Krivonos, “Split Casimir Operator and Universal Formulation of the Simple Lie Algebras”, Symmetry, 13:6 (2021), 1046

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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