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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 4, Pages 758–773 (Mi izv1203)  

This article is cited in 14 scientific papers (total in 14 papers)

Extremal projectors and generalized Mickelsson algebras over reductive Lie algebras

D. P. Zhelobenko


Abstract: A description is given of “extremal projectors” in the associative envelopes of reductive (finite-dimensional) Lie algebras. In terms of extremal projectors, a description is then obtained of (generalized) Mickelsson algebras. Finally, a characterization is given for these algebras in terms of generators and relations.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:1, 85–100

Bibliographic databases:

UDC: 519.46
MSC: Primary 17B20, 17B35; Secondary 81C40
Received: 11.12.1986

Citation: D. P. Zhelobenko, “Extremal projectors and generalized Mickelsson algebras over reductive Lie algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 52:4 (1988), 758–773; Math. USSR-Izv., 33:1 (1989), 85–100

Citation in format AMSBIB
\Bibitem{Zhe88}
\by D.~P.~Zhelobenko
\paper Extremal projectors and generalized Mickelsson algebras over reductive Lie algebras
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 4
\pages 758--773
\mathnet{http://mi.mathnet.ru/izv1203}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=966983}
\zmath{https://zbmath.org/?q=an:0671.17004|0659.17010}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 1
\pages 85--100
\crossref{https://doi.org/10.1070/IM1989v033n01ABEH000815}


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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. D. P. Zhelobenko, “$S$-algebras and Harish-Chandra modules over symmetric Lie algebras”, Math. USSR-Izv., 37:1 (1991), 1–17  mathnet  crossref  mathscinet  zmath  adsnasa
    2. D. P. Zhelobenko, “Constructive Modules and Extremal Projectors over Chevalley Algebras”, Funct. Anal. Appl., 27:3 (1993), 158–165  mathnet  crossref  mathscinet  zmath  isi
    3. D. P. Zhelobenko, “The algebra of quantum bosons, theb Shubert filtration, and Lusztig bases”, Russian Acad. Sci. Izv. Math., 43:3 (1994), 397–419  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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. P. Etingof, A. Varchenko, “Dynamical Weyl Groups and Applications”, Advances in Mathematics, 167:1 (2002), 74  crossref
    7. S. M. Khoroshkin, “Extremal Projector and Dynamical Twist”, Theoret. and Math. Phys., 139:1 (2004), 582–597  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Daniel S. Sage, Lawrence Smolinsky, “An explicit basis of lowering operators for irreducible representations of unitary groups”, Lithuanian J. Phys, 51:1 (2011), 5  crossref
    9. Shapovalov N.N., “Nekotorye obobscheniya konstruktsii obertyvayuschikh algebr i bilineinykh form na nikh”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2011, no. 5, 44–46  elib
    10. A. Shapiro, “Rational representations of the Yangian”, Journal of Geometry and Physics, 62:7 (2012), 1677  crossref
    11. Dmitry Artamonov, Valentina Goloubeva, “Noncommutative Pfaffians and classification of states of five-dimensional quasi-spin”, J. Math. Phys, 53:8 (2012), 083504  crossref
    12. Sergey Khoroshkin, Maxim Nazarov, Alexander Shapiro, “Rational and polynomial representations of Yangians”, Journal of Algebra, 418 (2014), 265  crossref
    13. Thomas Ashton, Andrey Mudrov, “R-matrix and Mickelsson algebras for orthosymplectic quantum groups”, J. Math. Phys, 56:8 (2015), 081701  crossref
    14. 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
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