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Trudy Mat. Inst. Steklov., 1950, Volume 36, Pages 3–288 (Mi tm1100)  

This article is cited in 36 scientific papers (total in 39 papers)

Unitary representations of the classical groups

I. M. Gel'fand, M. A. Naimark


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Citation: I. M. Gel'fand, M. A. Naimark, “Unitary representations of the classical groups”, Trudy Mat. Inst. Steklov., 36, Acad. Sci. USSR, Moscow–Leningrad, 1950, 3–288

Citation in format AMSBIB
\Bibitem{GelNai50}
\by I.~M.~Gel'fand, M.~A.~Naimark
\paper Unitary representations of the classical groups
\serial Trudy Mat. Inst. Steklov.
\yr 1950
\vol 36
\pages 3--288
\publ Acad. Sci. USSR
\publaddr Moscow--Leningrad
\mathnet{http://mi.mathnet.ru/tm1100}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=46370}
\zmath{https://zbmath.org/?q=an:0041.36206}


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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, “The analysis of irreducibility in the class of elementary representations of a complex semisimple Lie group”, Math. USSR-Izv., 2:1 (1968), 105–128  mathnet  crossref  mathscinet  zmath
    2. D. P. Zhelobenko, “Operational calculus on a complex semisimple Lie group”, Math. USSR-Izv., 3:5 (1969), 881–916  mathnet  crossref  mathscinet  zmath
    3. D. P. Zhelobenko, “Harmonic analysis of functions on semisimple Lie groups. II”, Math. USSR-Izv., 3:6 (1969), 1183–1217  mathnet  crossref  mathscinet  zmath
    4. A. N. Leznov, M. V. Saveliev, “Characters of the irreducible representations of the pseudounitary group $U(p,q)$. II”, Theoret. and Math. Phys., 4:3 (1970), 854–862  mathnet  crossref
    5. D. P. Zhelobenko, M. A. Naimark, “Description of the completely irreducible representations of a complex semisimple Lie group”, Math. USSR-Izv., 4:1 (1970), 59–83  mathnet  crossref  mathscinet  zmath
    6. S. I. Gel'fand, “Representations of the full linear group over a finite field”, Math. USSR-Sb., 12:1 (1970), 13–39  mathnet  crossref  mathscinet  zmath
    7. E. V. Kissin, “Razlozhenie tenzornogo proizvedeniya nekotorykh predstavlenii gruppy $SL(n,C)$ na neprivodimye predstavleniya”, UMN, 26:1(157) (1971), 225–226  mathnet  mathscinet  zmath
    8. A. N. Leznov, I. A. Fedoseev, “Representations of noncompact symplectic groups”, Theoret. and Math. Phys., 7:3 (1971), 546–560  mathnet  crossref  mathscinet  zmath
    9. A. N. Leznov, M. V. Saveliev, “Plancherel measure of the principal continuous series of unitary representations of $U(p, q)$”, Theoret. and Math. Phys., 82:2 (1971), 743–753  mathnet  crossref  mathscinet  zmath
    10. È. B. Vinberg, V. L. Popov, “On a class of quasihomogeneous affine varieties”, Math. USSR-Izv., 6:4 (1972), 743–758  mathnet  crossref  mathscinet  zmath
    11. M. H. Zakhar-Itkin, “The matrix Riccati differential equation and the semi-group of linear fractional transformations”, Russian Math. Surveys, 28:3 (1973), 89–131  mathnet  crossref  mathscinet  zmath
    12. S. G. Gindikin, A. A. Kirillov, D. B. Fuchs, “The work of I. M. Gel'fand on functional analysis, algebra and topology”, Russian Math. Surveys, 29:1 (1974), 5–35  mathnet  crossref  mathscinet  zmath
    13. G. I. Olshanskii, “Intertwining operators and complementary series in the class of representations induced from parabolic subgroups of the general linear group over a locally compact division algebra”, Math. USSR-Sb., 22:2 (1974), 217–255  mathnet  crossref  mathscinet  zmath
    14. M. A. Olshanetsky, A. M. Perelomov, “The Toda chain as a reduced system”, Theoret. and Math. Phys., 45:1 (1980), 843–854  mathnet  crossref  mathscinet  isi
    15. Klimyk A.I., “Infinitesimal Operators and Matrix–Elements of the Most Degenerate Series Representations of Groups”, Dopovidi Akademii Nauk Ukrainskoi Rsr Seriya A–Fiziko–Matematichni Ta Technichni Nauki, 1982, no. 11, 13–16  isi
    16. Ginzburg V.A., “Nilpotent Orbit Integral and Representations of Weyl Groups”, Doklady Akademii Nauk Sssr, 271:4 (1983), 780–783  mathnet  isi
    17. N. I. Nessonov, “A complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup”, Math. USSR-Sb., 58:1 (1987), 127–147  mathnet  crossref  mathscinet  zmath  isi
    18. Zelevinskii A.V., Retakh V.S., “The fundamental affine space and canonical basis in irreducible representations of the group $\mathrm{Sp}_4$”, Doklady Akademii Nauk Sssr, 300:1 (1988), 31–35  mathnet  isi
    19. D. V. Yur'ev, “A certain module over the binary-Lie central extension $\mathsf{jl_2}(\mathbb C)$ of the double $\mathsf{sl_2}(\mathbb C)+\mathsf{sl_2}(\mathbb C)$”, Russian Math. Surveys, 46:6 (1991), 233–234  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    20. Shatashvili S.L., “Correlation–Functions in the Itzykson–Zuber Model”, Communications in Mathematical Physics, 154:2 (1993), 421–432  crossref  isi
    21. Guhr T., “Gelfand–Tzetlin coordinates for the unitary supergroup”, Communications in Mathematical Physics, 176:3 (1996), 555–576  crossref  isi
    22. Yu. A. Neretin, “Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants”, Mosc. Math. J., 1:2 (2001), 157–220  mathnet  mathscinet  zmath  elib
    23. Yu. A. Neretin, “The action of an overalgebra on the Plancherel decomposition and shift operators in the imaginary direction”, Izv. Math., 66:5 (2002), 1035–1046  mathnet  crossref  crossref  mathscinet  zmath  elib
    24. “Teacher about His Disciple. Four Reviews by A. N. Kolmogorov on the Works of I. M. Gelfand (On the 90th Birthday of Izrail Moiseevich Gelfand)”, Funct. Anal. Appl., 37:4 (2003), 243–250  mathnet  crossref  crossref  mathscinet  zmath
    25. Yu. A. Neretin, “Rayleigh triangles and non-matrix interpolation of matrix beta integrals”, Sb. Math., 194:4 (2003), 515–540  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    26. Guhr T., Kohler H., “Angular gelfand–tzetlin coordinates for the supergroup UOSp(k(1)/2k(2))”, Journal of Mathematical Physics, 44:9 (2003), 4267–4286  crossref  isi
    27. S. V. Lyudkovskii, “Topological Transformation Groups of Manifolds over Non-Archimedean Fields, Their Representations, and Quasi-Invariant Measures, II”, Journal of Mathematical Sciences, 150:4 (2008), 2123–2223  mathnet  crossref  mathscinet  elib
    28. J. Math. Sci. (N. Y.), 141:4 (2007), 1452–1478  mathnet  crossref  mathscinet  zmath  elib
    29. Sergey É Derkachov, Alexander N. Manashov, “$\mathcal R$-Matrix and Baxter $\mathcal Q$-Operators for the Noncompact $\mathrm{SL}(N,\mathbb C)$ Invariant Spin Chain”, SIGMA, 2 (2006), 084, 20 pp.  mathnet  crossref  mathscinet  zmath
    30. Yu. A. Neretin, “$K$-Finite Matrix Elements of Irreducible Harish-Chandra Modules are Hypergeometric”, Funct. Anal. Appl., 41:4 (2007), 295–302  mathnet  crossref  crossref  mathscinet  zmath  isi
    31. 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
    32. S. E. Derkachev, A. N. Manashov, “General solution of the Yung–Baxter equation with symmetry group $\mathrm{SL}(\mathrm n,\mathbb C)$”, St. Petersburg Math. J., 21:4 (2010), 513–577  mathnet  crossref  mathscinet  zmath  isi
    33. David Karakhanyan, Roland Kirschner, “Jordan–Schwinger Representations and Factorised Yang–Baxter Operators”, SIGMA, 6 (2010), 029, 16 pp.  mathnet  crossref  mathscinet
    34. P. A. Valinevich, “Factorization of the $R$-matrix for the quantum algebra $U_q(s\ell_n)$”, J. Math. Sci. (N. Y.), 168:6 (2010), 811–819  mathnet  crossref
    35. M. V. Babich, S. E. Derkachov, “On rational symplectic parametrization of the coadjoint orbit of $\mathrm{GL}(N)$. Diagonalizable case”, St. Petersburg Math. J., 22:3 (2011), 347–357  mathnet  crossref  mathscinet  zmath  isi
    36. J. Math. Sci. (N. Y.), 209:6 (2015), 830–844  mathnet  crossref
    37. M. V. Babich, “Young tableaux and stratification of space of complex square matrices”, J. Math. Sci. (N. Y.), 213:5 (2016), 651–661  mathnet  crossref  mathscinet
    38. M. V. Babich, “Birational Darboux coordinates on nilpotent coadjoint orbits classical complex Lie groups, Jordan blocks $2\times2$”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 24, Zap. nauchn. sem. POMI, 465, POMI, SPb., 2017, 5–12  mathnet
    39. P. A. Valinevich, S. E. Derkachev, A. P. Isaev, “SOS-predstavlenie dlya $SL(2,\mathbb C)$-invariantnogo $R$-operatora i diagrammy Feinmana”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 24, Zap. nauchn. sem. POMI, 465, POMI, SPb., 2017, 82–104  mathnet
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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