Kevin Coulembier

Penrose tiling I am a Senior Lecturer in the School of Mathematics and Statistics at the University of Sydney, and a member of the Algebra Research Group.



Postal address: Kevin Coulembier
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia
Office: Room 632 Carslaw Building
Email: kevinc@maths.usyd.edu.au
Phone: +61 2 9351 3332


One of the main tourist attractions in Sydney is our weekly algebra seminar.


Forthcoming events: July 2018: Categorification and Higher Representation Theory, at the Institute Mittag Leffler (Stockholm).
October-November 2018 I will be visiting at MPIM in Bonn.
January 2019: Asia-Australia Algebra Conference in Western Sydney.



Research Interests

Papers

I. Representation theory of Lie (super)algebras

  1. K. Coulembier, V. Mazorchuk, X. Zhang: Indecomposable manipulations with simple modules in category O.
    To appear in Mathematical Research Letters
  2. K. Coulembier, V. Mazorchuk: Some homological properties of category O. IV.
    Forum Mathematicum 29 (2017), no. 5, 1083-1124.
  3. K. Coulembier, V. Serganova: Homological invariants in category O for the general linear superalgebra.
    Trans. Amer. Math. Soc. 369 (2017), no. 11, 7961-7997.
  4. S. Barbier, K. Coulembier: Polynomial realisations of Lie (super)algebras and Bessel operators.
    Int. Math. Res. Not. IMRN 2017, no. 10, 3148–3179.
  5. K. Coulembier, V. Mazorchuk : Dualities and derived equivalences for category O.
    Israel J. Math. 219 (2017), no. 2, 661–706.
  6. K. Coulembier, V. Mazorchuk: Primitive ideals, twisting functors and star actions for classical Lie superalgebras.
    J. Reine Angew. Math. 718 (2016), 207–253.
  7. K. Coulembier: The primitive spectrum of a basic classical Lie superalgebra.
    Comm. Math. Phys. 348 (2016), no. 2, 579-602.
  8. K. Coulembier, V. Mazorchuk: Some homological properties of category O. III.
    Adv. Math. 283 (2015) 204–231.
  9. K. Coulembier, I. Musson: The primitive spectrum for gl(m|n).
    Tohoku Math. J. (2) 70 (2018), no. 2, 225–266. 16 (17)
  10. K. Coulembier: Bott-Borel-Weil theory and Bernstein-Gelfand-Gelfand reciprocity for Lie superalgebras.
    Transform. Groups 21 (2016), no. 3, 681–723.
  11. K. Coulembier, V. Mazorchuk: Extension fullness of the categories of Gelfand-Zeitlin and Whittaker modules.
    SIGMA 11 (2015) 016, 17 pages.
  12. K. Coulembier, P. Somberg, V. Soucek: Joseph ideals and harmonic analysis for osp(m|2n).
    Int Math Res Notices 2014 (2014) 4291–4340.
  13. K. Coulembier: Bernstein-Gelfand-Gelfand resolutions for basic classical Lie superalgebras.
    Journal of Algebra 399 (2014) 131–169.
  14. K. Coulembier: On a class of tensor product representations for orthosymplectic superalgebras.
    J. Pure Appl. Algebra 217 (2013) 819–837.
  15. K. Coulembier: The orthosymplectic superalgebra in harmonic analysis.
    J. Lie Theory 23 (2013) 55–83.

II. Diagram algebras and related invariant theory

  1. K. Coulembier, R.B. Zhang: Borelic pairs for stratified algebras.
  2. K. Coulembier: The periplectic Brauer algebra.
    To appear in Proceedings of the LMS .
  3. K. Coulembier, M. Ehrig: The periplectic Brauer algebra II: decomposition multiplicities.
    J. Comb. Algebra 2 (2018), no. 1, 19–46.

III. Other aspects of representation theory

  1. K. Coulembier: Ringel duality and Auslander-Dlab-Ringel algebras.
    To appear in Journal of Pure and Applied Algebra.
  2. K. Coulembier, V. Mazorchuk: The G-centre and gradable derived equivalences.
    To appear in Journal of the Australian Mathematical Society
  3. S. Barbier, K. Coulembier: On structure and TKK algebras for Jordan superalgebras
    Communications in Algebra (2018), 46(2), 684-704.

IV. Invariant integration on (super)manifolds

  1. K. Coulembier, M. Kieburg: Pizzetti formulae for Stiefel manifolds and applications.
    Lett. Math. Phys. 105 (2015) no. 10, 1333–1376.
  2. K. Coulembier, R.B. Zhang: Invariant integration on orthosymplectic and unitary supergroups.
    J. Phys. A: Math. Theor. 45 (2012) 095204 (36 pp).
  3. K. Coulembier, H. De Bie, F. Sommen: Integration in superspace using distribution theory.
    J. Phys. A: Math. Theor. 42 (2009) 395206 (23pp).

V. Super and q-deformed differential operators

  1. K. Coulembier, H. De Bie: Conformal symmetries of the super Dirac operator.
    Rev. Mat. Iberoam. 31 (2015) no. 2, 373–410.
  2. K. Coulembier: The Fourier transform on quantum Euclidean space.
    SIGMA 7 (2011) 047 (30pp).
  3. K. Coulembier, H. De Bie: Hilbert space for quantum mechanics on superspace.
    J. Math. Phys. 52 (2011) 063504 (30 pp).
  4. K. Coulembier, H. De Bie, F. Sommen: Orthogonality of Hermite polynomials in superspace and Mehler type formulae.
    Proc. Lond. Math. Soc. (3) 103 (2011) 786–825.
  5. K. Coulembier, F. Sommen: Operator identities in q-deformed Clifford analysis.
    Adv. Appl. Clifford Algebr. 21 (2011) 677–696.
  6. K. Coulembier, H. De Bie, F. Sommen: Orthosymplectically invariant functions in superspace.
    J. Math. Phys. 51 (2010) 083504 (23pp).
  7. K. Coulembier, F. Sommen: q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials.
    J. Phys. A: Math. Theor. 43 (2010) 115202 (27pp).