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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
1950, Volume 36
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Unitary representations of the classical groups



This book is cited in the following Math-Net.Ru publications:
  1. A-Type Open ${\rm SL}(2,\mathbb{C})$ Spin Chain
    Pavel V. Antonenko, Sergey È. Derkachov, Pavel A. Valinevich
    SIGMA, 2025, 21, 107–48
  2. Factorization of the $\mathfrak{sl}(2|1)$ invariant R-matrix
    S. E. Derkachov, D. I. Getta
    Zap. Nauchn. Sem. POMI, 2025, 548, 70–100
  3. On representations of groups and algebras in spaces with indefinite metric
    E. V. Kissin, V. S. Shulman
    CMFD, 2021, 67:2, 295–315
  4. Deformation of the Poisson structure of a point particle due to gravitational back reaction
    D. A. Lyozin, A. N. Starodubtsev
    Zap. Nauchn. Sem. POMI, 2021, 509, 153–175
  5. Mellin–Barnes representation for $SL(2, \mathbb{C})$ magnet
    P. A. Valinevich
    Zap. Nauchn. Sem. POMI, 2020, 494, 125–143
  6. Construction of the Gelfand–Tsetlin basis for unitary principal series representations of the algebra $sl_n(\mathbb C)$
    P. A. Valinevich
    TMF, 2019, 198:1, 162–174
  7. The $6j$-symbols for the $SL(2,\mathbb C)$ group
    S. È. Derkachev, V. P. Spiridonov
    TMF, 2019, 198:1, 32–53
  8. Completeness of the $3j$-symbols for $SL(2,\mathbb C)$ group
    N. M. Belousov, S. È. Derkachev
    Zap. Nauchn. Sem. POMI, 2019, 487, 40–52
  9. SOS-representation for the $SL(2,\mathbb C)$-invariant $R$-operator and Feynman diagrams
    P. A. Valinevich, S. E. Derkachov, A. P. Isaev
    Zap. Nauchn. Sem. POMI, 2017, 465, 82–104
  10. Construction of eigenfunctions for a system of quantum minors of the monodromy matrix for an $SL(n,\mathbb C)$-invariant spin chain
    P. A. Valinevich, S. È. Derkachev, P. P. Kulish, E. M. Uvarov
    TMF, 2016, 189:2, 149–175
  11. Young tableaux and stratification of space of complex square matrices
    M. V. Babich
    Zap. Nauchn. Sem. POMI, 2015, 433, 41–64
  12. On birational Darboux coordinates on coadjoint orbits of classical complex Lie groups
    M. V. Babich
    Zap. Nauchn. Sem. POMI, 2015, 432, 36–57
  13. On rational symplectic parametrization of the coadjoint orbit of $\mathrm{GL}(N)$. Diagonalizable case
    M. V. Babich, S. E. Derkachov
    Algebra i Analiz, 2010, 22:3, 16–31
  14. Jordan–Schwinger Representations and Factorised Yang–Baxter Operators
    David Karakhanyan, Roland Kirschner
    SIGMA, 2010, 6, 29–16
  15. Factorization of the $R$-matrix for the quantum algebra $U_q(s\ell_n)$
    P. A. Valinevich
    Zap. Nauchn. Sem. POMI, 2010, 374, 92–106
  16. General solution of the Yung–Baxter equation with symmetry group $\mathrm{SL}(\mathrm n,\mathbb C)$
    S. E. Derkachev, A. N. Manashov
    Algebra i Analiz, 2009, 21:4, 1–94
  17. $K$-Finite Matrix Elements of Irreducible Harish-Chandra Modules are Hypergeometric
    Yu. A. Neretin
    Funktsional. Anal. i Prilozhen., 2007, 41:4, 60–69
  18. Topological Transformation Groups of Manifolds over Non-Archimedean Fields, Their Representations, and Quasi-Invariant Measures, II
    S. V. Lyudkovskii
    CMFD, 2006, 18, 5–100
  19. $\mathcal R$-Matrix and Baxter $\mathcal Q$-Operators for the Noncompact $\mathrm{SL}(N,\mathbb C)$ Invariant Spin Chain
    Sergey É Derkachov, Alexander N. Manashov
    SIGMA, 2006, 2, 84–20
  20. Notes on Stein–Sahi representations and some problems of non-$L^2$-harmonic analysis
    Yu. A. Neretin
    Zap. Nauchn. Sem. POMI, 2006, 331, 125–169
  21. Rayleigh triangles and non-matrix interpolation of matrix beta integrals
    Yu. A. Neretin
    Mat. Sb., 2003, 194:4, 49–74
  22. The action of an overalgebra on the Plancherel decomposition and shift operators in the imaginary direction
    Yu. A. Neretin
    Izv. RAN. Ser. Mat., 2002, 66:5, 171–182
  23. Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants
    Yu. A. Neretin
    Mosc. Math. J., 2001, 1:2, 157–220
  24. A certain module over the binary-Lie central extension $\mathsf{jl_2}(\mathbb C)$ of the double $\mathsf{sl_2}(\mathbb C)+\mathsf{sl_2}(\mathbb C)$
    D. V. Yur'ev
    Uspekhi Mat. Nauk, 1991, 46:6(282), 223–224
  25. A complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup
    N. I. Nessonov
    Mat. Sb. (N.S.), 1986, 130(172):2(6), 131–150
  26. The Toda chain as a reduced system
    M. A. Olshanetsky, A. M. Perelomov
    TMF, 1980, 45:1, 3–18
  27. 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
    G. I. Olshanskii
    Mat. Sb. (N.S.), 1974, 93(135):2, 218–253
  28. The matrix Riccati differential equation and the semi-group of linear fractional transformations
    M. H. Zakhar-Itkin
    Uspekhi Mat. Nauk, 1973, 28:3(171), 83–120
  29. On a class of quasihomogeneous affine varieties
    È. B. Vinberg, V. L. Popov
    Izv. Akad. Nauk SSSR Ser. Mat., 1972, 36:4, 749–764
  30. A decomposition of the tensor product of certain representations of the group $SL(n,C)$ into irreducible representations
    È. V. Kissin
    Uspekhi Mat. Nauk, 1971, 26:1(157), 225–226
  31. Plancherel measure of the principal continuous series of unitary representations of $U(p, q)$
    A. N. Leznov, M. V. Saveliev
    TMF, 1971, 8:2, 161–174
  32. Representations of noncompact symplectic groups
    A. N. Leznov, I. A. Fedoseev
    TMF, 1971, 7:3, 298–317
  33. Description of the completely irreducible representations of a complex semisimple Lie group
    D. P. Zhelobenko, M. A. Naimark
    Izv. Akad. Nauk SSSR Ser. Mat., 1970, 34:1, 57–82
  34. Representations of the full linear group over a finite field
    S. I. Gel'fand
    Mat. Sb. (N.S.), 1970, 83(125):1(9), 15–41
  35. Characters of the irreducible representations of the pseudounitary group $U(p,q)$. II
    A. N. Leznov, M. V. Saveliev
    TMF, 1970, 4:3, 310–321
  36. Harmonic analysis of functions on semisimple Lie groups. II
    D. P. Zhelobenko
    Izv. Akad. Nauk SSSR Ser. Mat., 1969, 33:6, 1255–1295
  37. Operational calculus on a complex semisimple Lie group
    D. P. Zhelobenko
    Izv. Akad. Nauk SSSR Ser. Mat., 1969, 33:5, 931–973
  38. The analysis of irreducibility in the class of elementary representations of a complex semisimple Lie group
    D. P. Zhelobenko
    Izv. Akad. Nauk SSSR Ser. Mat., 1968, 32:1, 108–133


  39. Mathematical works of D. P. Zhelobenko
    Yu. A. Neretin, S. M. Khoroshkin
    Uspekhi Mat. Nauk, 2009, 64:1(385), 178–188
  40. 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)
    Funktsional. Anal. i Prilozhen., 2003, 37:4, 3–12
  41. 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)
    Funktsional. Anal. i Prilozhen., 2003, 37:4, 3–12
  42. 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)
    Funktsional. Anal. i Prilozhen., 2003, 37:4, 3–12
  43. The work of I. M. Gel'fand on functional analysis, algebra and topology
    S. G. Gindikin, A. A. Kirillov, D. B. Fuchs
    Uspekhi Mat. Nauk, 1974, 29:1(175), 195–223

© Steklov Math. Inst. of RAS, 2026