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TMF, 1971, Volume 8, Number 2, Pages 255–271 (Mi tmf4403)  

This article is cited in 7 scientific papers (total in 8 papers)

Projection operators for simple lie groups

R. M. Asherova, Yu. F. Smirnov, V. N. Tolstoy


Abstract: The solution of many problems in nuclear theory and elementary particle physics amounts to decomposing the reducible representations of the symmetry groups of quantum mechanical systems into irreducible components. To carry out this decomposition, projection operators are needed. In the present paper we have constructed, for all simple compact Lie groups $G(l)$ of the rank $l$ (both classical and exceptional), operators which project the arbitrary vector with the weight $f=(f_1,f_2,…,f_l)$ onto the highest weight vector of the irreducible representation $D^{[f]}$ of the group $G(l)$. The projection operators are represented in the form of series composed of powers of the infinitesimal operators, which makes them convenient for the solution of particular problems concerning the decomposition of reducible representations into irreducible components. The structure of the projection operators is given for all simple compact Lie groups by similar formulas.

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English version:
Theoretical and Mathematical Physics, 1971, 8:2, 813–825

Bibliographic databases:

Received: 02.12.1970

Citation: R. M. Asherova, Yu. F. Smirnov, V. N. Tolstoy, “Projection operators for simple lie groups”, TMF, 8:2 (1971), 255–271; Theoret. and Math. Phys., 8:2 (1971), 813–825

Citation in format AMSBIB
\Bibitem{AshSmiTol71}
\by R.~M.~Asherova, Yu.~F.~Smirnov, V.~N.~Tolstoy
\paper Projection operators for simple lie groups
\jour TMF
\yr 1971
\vol 8
\issue 2
\pages 255--271
\mathnet{http://mi.mathnet.ru/tmf4403}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=475353}
\zmath{https://zbmath.org/?q=an:0223.22019}
\transl
\jour Theoret. and Math. Phys.
\yr 1971
\vol 8
\issue 2
\pages 813--825
\crossref{https://doi.org/10.1007/BF01038003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. M. Asherova, Yu. F. Smirnov, V. N. Tolstoy, “Projection operators for simple lie groups”, Theoret. and Math. Phys., 15:1 (1973), 392–401  mathnet  crossref  mathscinet  zmath
    2. A. N. Leznov, M. V. Saveliev, “Projection operators for semisimple Lie groups”, Theoret. and Math. Phys., 31:2 (1977), 456–457  mathnet  crossref  mathscinet  zmath
    3. D. P. Zhelobenko, “Extremal projectors and generalized Mickelsson algebras over reductive Lie algebras”, Math. USSR-Izv., 33:1 (1989), 85–100  mathnet  crossref  mathscinet  zmath
    4. D. V. Yur'ev, “Topics in isotopic pairs and their representations. II. A general supercase”, Theoret. and Math. Phys., 111:1 (1997), 511–518  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. D. P. Zhelobenko, “Universal Verma modules and $W$-resolvents over Kač–Moody algebras”, Theoret. and Math. Phys., 122:3 (2000), 278–297  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Yu. A. Neretin, S. M. Khoroshkin, “Mathematical works of D. P. Zhelobenko”, Russian Math. Surveys, 64:1 (2009), 187–198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. A. I. Mudrov, “Regularization of Mickelsson generators for nonexceptional quantum groups”, Theoret. and Math. Phys., 192:2 (2017), 1205–1217  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Andrey I. Mudrov, “Contravariant Form on Tensor Product of Highest Weight Modules”, SIGMA, 15 (2019), 026, 10 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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