Joseph BERNSTEIN
LIST OF PUBLICATIONS

  1. J. Bernstein
    On sets covered up by segments
    Doklady Akad. Nauk (Soviet Mathematics – Doklady) 146, No.1, 11-13 (1962)(In Russian).PDF

  2. J. Bernstein, S. Panov
    Algorithm for decision of the routing problem.
    Economic and Mathematical Methods, Vol. 2, No. 5,Moscow,711-722 (1966) (In Russian).PDF

  3. J. Bernstein
    On the dimension of commutative sub-rings of R(n,k).
    Functional Analysis and its Applications 1, No.4, 79-81 (1967).PDF

  4. J. Bernstein
    Meromorphic continuation of function fλ for some polynomials f.
    Functional Analysis and its Applications, No.1, 92-93 (1968).PDF

  5. J. Bernstein, S.I. Gelfand
    Meromorphic continuation of the function Pλ.
    Functional Analysis and its Applications 3, No.1, 84-85 (1969).PDF

  6. J. Bernstein, D. Kazhdan
    On 1-dimensional cohomologies of discrete subgroups.
    Functional Analysis and its Applications 4, No.1, 1-5 (1970).PDF

  7. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Differential operators on the principal affine space.
    Doklady Akad. Nauk 195, No.6, 1255-1258 (1970).PDF

  8. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Structure of representations generated by highest weight vectors.
    Functional Analysis and its Applications 5, No.1, 1-9 (1971).PDF

  9. J. Bernstein
    Modules over the ring of differential operators; the study of
    fundamental solutions of equations with constant coefficients.
    Functional Analysis and its Applications 5, No.2, 1-16 (1971).PDF

  10. J. Bernstein
    Analytic continuation of distributions with respect to a parameter.
    Functional Analysis and its Applications 6, No.4, 26-40 (1972).PDF

  11. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Differential operators on the cubic cone.
    Uspekhi Mat. Nauk (Soviet Mathematics – Surveys) 37, No.1, 185-190 (1972).PDF

  12. J. Bernstein, B.I. Rosenfeld
    On characteristic classes of foliations.
    Functional Analysis and its Applications 6, No.1, 68-69 (1972).PDF

  13. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Schubert cells and cohomologies of flag manifolds.
    Functional Analysis and its Applications 7, No.1, 64-65 (1973).PDF

  14. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Schubert cells and cohomologies of spaces G∕P.
    Uspekhi Mat. Nauk 38, No.3, 3-26(1973).PDF

  15. J. Bernstein, I.M. Gelfand, V.A. Ponomarev
    Coxeter functors and Gabriel’s theorem.
    Uspekhi Mat. Nauk 38, No.2, 19-33(1973).PDF

  16. J. Bernstein, B.I. Rozenfeld
    Homogeneous spaces for infinite dimensional
    Lie algebras and characteristic classes of foliations.
    Uspekhi Mat. Nauk 28, No.4, 103-138 (1973).PDF

  17. G.M. Adel’son-Velski, J. Bernstein, M.L. Gerver
    Estimation of the number of actions for the partial determination of an order of a finite set of numbers.
    Studies in Discrete Mathematics, Izdat ”Nauka”,Moscow,184-188 (1973) (In Russian).

  18. J. Bernstein
    All reductive p-adic groups are tame.
    Functional Analysis and its Applications 8, No.2, 3-6 (1974).PDF

  19. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    A new model for the representations of finite semisimple algebraic groups
    Uspekhi. Mat. Nauk 29, No. 3, 185-186 (1974).PDF

  20. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Models of representations of compact Lie groups
    Functional Analysis and its Applications 9, No.4, 61-62 (1975).PDF

  21. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Differential operators on principal affine space and study of g-modules.
    In ”Lie groups and their representations” (I.M.Gelfand ed)
    Akademiai Kiado, Budapest 21-64 (1975).PDF

  22. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    On some category of g-modules.
    Functional Analysis and its Applications 10, No.2, 1-8 (1976).PDF

  23. J. Bernstein, A.V. Zelevinsky
    Representations of the group GL(n,F), where F is a local non-Archimedean field.
    Uspekhi Mat. Nauk 10, No.3, 5-70 (1976).PDF

  24. J. Bernstein, A.V. Zelevinsky
    Induced representations of GL(n) over p-adic field.
    Functional Analysis and its Applications 10, No.3, 74-75 (1976).PDF

  25. J. Bernstein, A.V. Zelevinsky
    Induced representations of reductive p-adic groups. I.
    Ann. Scient. Ec. Norm. Sup. 10, No.4, 441-472 (1977).PDF

  26. J. Bernstein, D.A. Leites
    Integral forms and Stokes formula on supermanifolds.
    Functional Analysis and its Applications 11, No.1, 55-56 (1977).PDF

  27. J. Bernstein, D.A. Leites
    How to intergrate differential forms on supermanifolds.
    Functional Analysis and its Applications 11, No.3, 70-71 (1977).PDF

  28. J. Bernstein, D.N. Bernstein, V.K. Dubrovich
    On relict recombination lines.
    Soviet Astronomy 54, No.4 (1977).

  29. J. Bernstein, M.L. Gerver
    A problem of integral geometry for a family of geodesics and an inverse kinematics seismics problem
    Doklad. Akad. Nauk, SSSR, Vol. 243 No. 2, 302-305 (1978)(In Russian).PDF, full text PDF.

  30. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Local structure of the category of Harish-Chandra modules. Part I
    C.R.Acad. Sci. 286, No. 10, A435-A437 (1978).PDF

  31. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Local structure of the category of Harish-Chandra modules. Part II
    C.R.Acad. Sci. 286, No. 10, A435-A437 (1978).PDF

  32. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Algebraic bundles on Pn and problems of linear algebra.
    Functional Analysis and its Applications 12, No.3, 66-67 (1978).PDF

  33. J. Bernstein (under the pseudonym I.Yantarov)
    Commuting polinomials.
    Kvant, No.4, 1-11 (1979).(in Russian)PDF(in English)PDF

  34. J. Bernstein, O.V. Shvartsman
    Chevalley theorem for complex cristallographic Coxeter groups.
    Functional Analysis and its Applications 12, No.4, 79-80 (1978).PDF

  35. J. Bernstein, D.A. Leites
    The characters formula for irreducible finite dimensional representations of Lie superalgebra GL(n,1) and SL(n,1).
    Comp. Rendues de l’Acad. Bulgare 33, No.8, 277-278 (1980).

  36. J. Bernstein, S.I. Gelfand
    Tensor products of finite and infinite dimensional representations of semisimple Lie algebras.
    Comp. Mathematica 41, No.2, 245-285 (1980).PDF

  37. J. Bernstein, V.F. Shvartsman
    On the connection between the size of the Universe and its curvature.
    JETP 78, No.11, 1617-1628 (1980).PDF

  38. A. Beilinson, J. Bernstein
    Localization de g-modules.
    Comp. Rend. Acad. Sci. Paris t.292, 15-18 (1981).PDF

  39. J. Bernstein, I.M. Gelfand, S.I. Gelfand
    Models of representations of Lie groups.
    Trudy Sem. Petrovsk 2, 3-21 (1976) (also: Selecta Math. Soviet, 1, No. 2, (1981)).PDF

  40. J. Bernstein, D.A. Leites
    Invariant differential operators and irreducible representations of Lie superalgebras of vector fields.
    Serdica 7, No. 4, 320-334 (1981) (Selecta Math. Soviet 1, No. 2, 143-160 (1981)).PDF

  41. J. Bernstein, D.A. Leites
    The superalgebra Q(n), the odd trace and the odd determinant.
    C.R. Acad. Bulgare. 35, No. 3, 285-286 (1982).

  42. A. Beilinson, J. Bernstein
    A generalization of Casselman’s submodule theorem.
    In Proceedings of the conference ”Representations of reduvtive Lie groups”,
    Park City, UTAH, April (1982),
    Progr. Math. 40,35-52,Birkh”auzer,Boston,Mass (1983).PDF

  43. J. Bernstein, D.A. Leites
    Irreducible representations of finite-dimensional Lie superalgebras of type W.
    Selecta Math. Soviet 3, No. 1, 63-68 (1983/84).

  44. A.A. Beilinson, J. Bernstein, P. Deligne
    Faisceux pervers.
    Asterisque 100, 3-171 (1983).PDF

  45. J. Bernstein
    P-invariant distributions on GL(n) and the classification of unitary representations of GL(n) (non-Archimedean case).
    Springer Lecture Notes in Math. 943, 50-102 (1984).PDF

  46. J. Bernstein, P. Deligne
    Le ”centre” de Bernstein,
    In ”Representations des groups redutifs sur un corps local,
    Traveaux en cours” (P.Deligne ed.), Hermann, Paris, 1-32 (1984).PDF

  47. J. Bernstein, P. Deligne, D. Kazhdan
    Trace Paley Wiener theorem for reductive p-adic groups.
    Jour. d’Analyse Math. 47, 180-192 (1986).PDF

  48. J. Bernstein, V. Lunts
    On non-holonomic irreducible D-modules.
    Invent. Math. 94, 223-243 (1988).PDF

  49. J. Bernstein
    On the support of Plancherel measure.
    Jour. of Geom. and Physics 5, No.4 (1988).PDF

  50. J. Bernstein
    Trace in categories.
    In the book ”Operator algebras, Unitary representations, Enveloping algebras and Invariant theory ”, May 1989,
    Progr.Math.92,417-424,Birkh”auser,Boston(1990).PDF

  51. J. Bernstein,
    Representations of p-adic groups
    Lectures by Joseph Bernstein. Written by Karl E. Rumelhart.
    Harvard University. (Fall 1992).PDF

  52. A.A. Beilinson, J. Bernstein
    A proof of the Jantzen conjectures.
    Advances in Soviet Mathematics 16:1, 1-50 (1993) Issue in honor of I.M.Gelfand.PDF

  53. J. Bernstein, V. Lunts
    Equivariant sheaves and functors.
    Lecture Notes in Mathematics, v.1578 (1994), 1-139. 1 2 3 4 5 6

  54. G.M. Adel’son-Velski, J. Bernstein, M.L. Gerver
    Who will go to Rio?
    Kvant, No.1, 1-9 (1995).(in Russian)PDF

  55. J. Bernstein, V. Lunts
    Localization for derived categories of (g,K)-modules
    Jour. Amer. Math. Society, v.8 , no.4 (1995), 819-856.PDF

  56. J. Bernstein, T. Khovanova
    On the Quantum Group SLq(2)
    Comm. in Math. Physics, v.177 (1996), 691-708.PDF

  57. J. Bernstein, V. Lunts
    A simple proof of Kostant’s theorem that U(g) is free over its center.
    Amer. Jour. Math. v.118, no.5 (1996), 979-987.PDF

  58. J.Bernstein, A.Braverman, D.Gaitsgory
    The Cohen-Macaulay property of the category of (g,K)- modules
    Selecta Mathematica, New Ser. v.3 (1997), 303-314.PDF

  59. J.  Bernstein, A.  Reznikov
    Sobolev norms of automorphic functionals and Fourier coefficients of cusp forms,
    Comptes Rendues Acad. Sci. Paris, t.327,1998 Ser.1, p.111-116.PDF

  60. J. Bernstein
    Analytic structures on representation spaces of reductive groups
    Documenta Mathematica, Proceedings of the ICM, Berlin 1998, v. 2, 519-525.PDF

  61. J. Bernstein, A. Reznikov
    Analytic continuation of representations and estimates of automorphic forms,
    Annals of Mathematics. 150 (1999), 329-352.PDF

  62. J. Bernstein, I. Frenkel, M. Khovanov.
    A categorification of the Temperley-Lieb algebra and Schur quotients of U(sl2) via projective and Zuckerman functors,
    Selecta Math (N.S.) 5 (1999), no. 2, 199-241.PDF

  63. J. Bernstein, A. Reznikov
    Sobolev norms of automorphic functionals,
    Internat. Math. Res. Notices, 2002:40, 2155-2174 (2002).PDF

  64. J. Bernstein, S.Gindikin,
    Notes on Integral Geometry for Manifolds of Curves,
    American Mathematical Society Translations, Vol.210, 57-79, (2003).PDF

  65. J. Bernstein, A. Reznikov,
    Estimates of Automorphic Functions,
    Moscow Mathematical Journal - v.4(2004), no.2, 19-37.PDF

  66. S. Alesker , J. Bernstein
    Range characterization of the cosine transform on higher Grassmannians,
    Advances in Mathematics - Adv. Math. 184(2004), no.2, 367-379.PDF

  67. J. Bernstein, A. Reznikov
    Periods, Subconvexity of L-functions and Representation Theory,
    Journal of Differential Geometry - v.70,no.1 (May 2005), 129-142.PDF

  68. J.Bernstein, O.Schwarzman
    Complex crystallographic Coxeter groups and affine root systems. J. Nonlinear Math. Phys. 13 (2006), no. 2, 163–182.PDF

  69. J.Bernstein, O.Schwarzman
    Chevalley’s theorem for the complex crystallographic groups. J. Nonlinear Math. Phys. 13 (2006), no. 3, 323-351.PDF

  70. J. Bernstein, A. Reznikov
    Subconvexity bounds for triple L-functions and Representation Theory,
    Annals of Mathematics, no. 172 (2010), 1679-1718. PDF

  71. J. Bernstein
    Lectures on Lie Algebras
    Representation Theory, Complex Analysis and Integral Geometry, Birkhauser (2012), 97-133. PDF

  72. J. Bernstein, Bernhard Krotz
    Smooth Frechet Globalizations Of Harish-Chandra Modules
    Israel Journal of Mathematics 199 (1), 2014, 45 - 111. PDF

  73. J. Bernstein, Andre Reznikov
    Periods and Global Invariants of Automorphic Representations
    Journal of Number Theory, v. 243, February 2023, pp 117 - 159 DOI:10.1016/j.jnt.2022.07.010
    arXiv:1312.2898v2 [math.NT] 23 Sep 2014. PDF

  74. J. Bernstein
    Stacks in Representation Theory
    arXiv:1410.0435v3 [math.RT] 12 May 2016.
    Tsinghua lectures in mathematics
    ISBN:978-7-04-050714-0 2018-12-06, ALM 45, pp.123-139 PDF

  75. J. Bernstein, Nigel Higson and Eyal Subag
    Algebraic Families of Harish-Chandra Pairs
    International Mathematics Research Notices, Volume 2020, Issue 15, August 2020, Pages 47764808, https://doi.org/10.1093/imrn/rny147
    arXiv:1610.03435v1 [math.RT] 11 Oct 2016. PDF

  76. J. Bernstein, Roman Bezrukavnikov, David Kazhdan
    Deligne-Lusztig Duality and Wonderful Compactification
    arXiv:1701.07329v2 [math.RT] 14 Feb 2017. PDF

  77. Joseph Bernstein, Nigel Higsony and Eyal Subag
    Contractions of Representations and Algebraic Families of Harish-Chandra Modules
    International Mathematics Research Notices, Volume 2020, Issue 11, June 2020, Pages 34943520, https://doi.org/10.1093/imrn/rny146
    arXiv:1703.04028v2 [math.RT] 10 Sep 2017. PDF

  78. J. Bernstein, Erez Lapid
    On the meromorphic continuation of Eisenstein series
    Journal of the American Mathematical Society (2023) Volume 37, Number 1, January 2024, Pages 187234 https://doi.org/10.1090/jams/1020
    arXiv:1911.02342v2 [math.RT] 27 Apr 2020. PDF

  79. J. Bernstein
    Hidden Sign in the Langlands Correspondence
    arXiv:2004.10487v2 [math.RT] 19 May 2020. PDF

  80. A. Aizenbud, J. Bernstein, E. Sayag
    Strong density of spherical characters attached to unipotent subgroups
    arXiv:2202.04984v1 [math.RT] 10 Feb 2022. PDF

  81. J. Bernstein, D. Gourevitch, S. Sahi
    Hypergeometric Orthogonal Polynomials of Jacobi Type
    arXiv:2401.14715v1 [math.CA] 26 Jan 2024. PDF