Kevin Coulembier

Penrose tiling I am an Associate Professor in the School of Mathematics and Statistics at the University of Sydney,
and a member of the Algebra Research Group.
My CV is here.


Postal address: Kevin Coulembier
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia
Office: Room 717 Carslaw Building
Email: first name dot last name @ sydney.edu.au


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

I am an editor for Annals of Representation Theory and Mathematische Zeitschrift.

Students interested in taking the Topics in Algebra course in Semester 2 (2024) can find the preliminary outline here.


Forthcoming events: January 2024: Symmetric Tensor Categories and Representation Theory, Los Angeles
July 2024: Representations of Supergroups, Bonn
November 2024: Matrix Program: Tensor categories, quantum symmetries and mathematical physics, Melbourne

Research Interests

Papers

I. Representation theory of Lie (super)algebras

  1. K. Coulembier, P. Etingof, A. Kleshchev, V. Ostrik : Super invariant theory in positive characteristic.
    Eur. J. Math.9 (2023), no. 4, Ppaer No. 94, 39pp.
  2. S.-J. Cheng, K. Coulembier: Representation theory of a semisimple extension of the Takiff superalgebra.
    IMRN2022, no. 18, 14454 - 14495.
  3. C.-W. Chen, S.-J. Cheng, K. Coulembier: Tilting modules for classical Lie superalgebras.
    J. Lond. Math. Soc. (2) 103 (2021), no. 3, 870-900.
  4. C.-W. Chen, K. Coulembier: The primitive spectrum and category O for the periplectic Lie superalgebra.
    Canad. J. Math. 72 (2020), no. 3, 625-655.
  5. K. Coulembier: The classification of blocks in BGG category O.
    Math. Z. 295 (2020), no. 1-2, 821-837.
  6. C.W. Chen, K. Coulembier, V. Mazorchuk: Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras.
    Math. Z. 297 (2021), no. 1-2, 255–281.
  7. K. Coulembier, I. Penkov: On an infinite limit of BGG categories O.
    Mosc. Math. J. 19 (2019), no. 4, 655-693.
  8. K. Coulembier, V. Mazorchuk, X. Zhang: Indecomposable manipulations with simple modules in category O.
    Mathematical Research Letters, 26(2), 447-499.
  9. K. Coulembier, V. Mazorchuk: Some homological properties of category O. IV.
    Forum Mathematicum 29 (2017), no. 5, 1083-1124.
  10. K. Coulembier, V. Serganova: Homological invariants in category O for the general linear superalgebra.
    Trans. Amer. Math. Soc. 369 (2017), no. 11, 7961-7997.
  11. S. Barbier, K. Coulembier: Polynomial realisations of Lie (super)algebras and Bessel operators.
    Int. Math. Res. Not. IMRN 2017, no. 10, 3148–3179.
  12. K. Coulembier, V. Mazorchuk : Dualities and derived equivalences for category O.
    Israel J. Math. 219 (2017), no. 2, 661–706.
  13. K. Coulembier, V. Mazorchuk: Primitive ideals, twisting functors and star actions for classical Lie superalgebras.
    J. Reine Angew. Math. 718 (2016), 207–253.
  14. K. Coulembier: The primitive spectrum of a basic classical Lie superalgebra.
    Comm. Math. Phys. 348 (2016), no. 2, 579-602.
  15. K. Coulembier, V. Mazorchuk: Some homological properties of category O. III.
    Adv. Math. 283 (2015) 204–231.
  16. K. Coulembier, I. Musson: The primitive spectrum for gl(m|n).
    Tohoku Math. J. (2) 70 (2018), no. 2, 225–266. 16 (17)
  17. K. Coulembier: Bott-Borel-Weil theory and Bernstein-Gelfand-Gelfand reciprocity for Lie superalgebras.
    Transform. Groups 21 (2016), no. 3, 681–723.
  18. K. Coulembier, V. Mazorchuk: Extension fullness of the categories of Gelfand-Zeitlin and Whittaker modules.
    SIGMA 11 (2015) 016, 17 pages.
  19. K. Coulembier, P. Somberg, V. Soucek: Joseph ideals and harmonic analysis for osp(m|2n).
    Int Math Res Notices 2014 (2014) 4291–4340.
  20. K. Coulembier: Bernstein-Gelfand-Gelfand resolutions for basic classical Lie superalgebras.
    Journal of Algebra 399 (2014) 131–169.
  21. K. Coulembier: On a class of tensor product representations for orthosymplectic superalgebras.
    J. Pure Appl. Algebra 217 (2013) 819–837.
  22. K. Coulembier: The orthosymplectic superalgebra in harmonic analysis.
    J. Lie Theory 23 (2013) 55–83.

II. Monoidal categories

  1. K. Coulembier, P. Etingof and V. Ostrik : On Frobenius exact symmetri tensor categories. With an appendix by A. Kleshchev.
    Annals of Mathematics (2) 197 (2023), no. 3, 1235 - 1279.
  2. K. Coulembier: Additive Grothendieck pretopologies and presentations of tensor categories
    Appl. Categ. Structures 31 (2023), no. 3, Paper No. 23, 41pp.
  3. K. Coulembier: Homological kernels of monoidal functors
    Selecta Mathematica 29, nu 24 (2023).
  4. K. Coulembier, P. Etingof, V. Ostrik and B. Pauwels: Monoidal abelian envelopes with a quotient property.
    J. Reine Angew. Math. 794 (2023), 179 - 214.
  5. K. Coulembier, I. Entova-Aizenbud and T. Heidersdorf : Monoidal abelian envelopes and a conjecture of Benson--Etingof
    Algebra and Number Theory 16 (2022), no. 9, 2099 - 2117.
  6. K. Coulembier: Monoidal abelian envelopes.
    Compos. Math. 157 (2021), no. 7, 1584-1609.
  7. K. Coulembier: Tannakian categories in positive characteristic.
    Duke Math. J. 169 (2020), no. 16, 3167-3219.
  8. K. Coulembier, R. Street and M. Van den Bergh : Freely adjoining monoidal duals
    Math. Structures Comput. Sci. 31 (2021), no. 7, 748–768.
  9. K. Coulembier and P. Etingof: Maximal Tannakian subcategories, Appendix to P. Etingof, S. Gelaki: Finite symmetric integral tensor categories with the Chevalley property.
    Int. Math. Res. Not. IMRN 2021, no. 12, 9083-9121.

III. Diagram algebras and related invariant theory

  1. K. Coulembier, M. Ehrig: The periplectic Brauer algebra III: Deligne category.
    Algebr. Represent. Theory 24 (2021), no. 4, 993–1027.
  2. K. Coulembier: Ringel duals of Brauer algebras via super groups.
    Int. Math. Res. Not. IMRN 2021, no. 5, 3512-3542.
  3. K. Coulembier: Tensor ideals, Deligne categories and invariant theory.
    Selecta Math. (N.S.) 24 (2018), no. 5, 4659-4710.
  4. K. Coulembier, R.B. Zhang: Borelic pairs for stratified algebras.
    Adv. Math. 345 (2019), 53–115.
  5. K. Coulembier: The periplectic Brauer algebra.
    Proc. Lond. Math. Soc. (3) 117 (2018), no. 3, 441-482.
  6. K. Coulembier, M. Ehrig: The periplectic Brauer algebra II: decomposition multiplicities.
    J. Comb. Algebra 2 (2018), no. 1, 19–46.

IV. Other aspects of representation theory

  1. K. Coulembier: Some homological properties of highest weight categories and ind-completions.
    J. Algebra 562 (2020), 341–367.
  2. K. Coulembier: Ringel duality and Auslander-Dlab-Ringel algebras.
    J. Pure Appl. Algebra 222 (2018), no. 12, 3831–3848.
  3. K. Coulembier, V. Mazorchuk: The G-centre and gradable derived equivalences.
    J. Aust. Math. Soc. 105 (2018), no. 3, 289–315.
  4. S. Barbier, K. Coulembier: On structure and TKK algebras for Jordan superalgebras
    Communications in Algebra (2018), 46(2), 684-704.

V. 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).

VI. 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).