Publications (Last updated August 2015)

In preparation

  1. Actions, slices and radial parts for superspaces. (with A. Alldridge)

  2. Reductive symmetric superpairs and restriction theorems. (with A. Alldridge)

  3. Some homological properties of the category O. IV. (with V. Mazorchuk)

  4. Polynomial realisations of Lie (super)algebras and Bessel operators. (with S. Barbier)

Preprints

  1. K. Coulembier and V. Mazorchuk, Dualities and derived equivalences for category O. arXiv:1506.08590.

  2. K. Coulembier and V. Serganova, Homological invariants in category O for the general linear superalgebra. arXiv:1501.01145.

  3. K. Coulembier and I. Musson, The primitive spectrum for gl(m|n). arXiv:1409.2532.

  4. K. Coulembier, Bott-Borel-Weil theory, BGG reciprocity and twisting functors for Lie superalgebras. arXiv:1404.1416.

A1-papers

  1. K. Coulembier and V. Mazorchuk, Some homological properties of the category O. III. Adv. Math. 283 (2015), 204-231.

  2. K. Coulembier and M. Kieburg, Pizzetti formulae for Stiefel manifolds and applications. Accepted in Letters in Mathematical Physics. doi: 10.1007/s11005-015-0774-x.

  3. K. Coulembier and V. Mazorchuk, Extension fullness of the categories of Gelfand-Zeitlin and Whittaker modules. SIGMA 11 (2015), 016, 17 pages.

  4. K. Coulembier and V. Mazorchuk, Primitive ideals, twisting functors and star actions for classical Lie superalgebras. Accepted in J. Reine Ang. Math. doi: 10.1515/crelle-2014-0079.

  5. K. Coulembier and H. De Bie, Conformal invariance of the super Dirac operator. Rev. Mat. Iberoam. 31 (2015), no. 2, 373-410.

  6. K. Coulembier, Bernstein-Gelfand-Gelfand resolutions for basic classical Lie superalgebras. J. Algebra 399 (2014), 131-169.

  7. K. Coulembier, P. Somberg and V. Soucek, Joseph ideals and harmonic analysis for osp(m|2n). Int. Math. Res. Not. IMRN (2014), no. 15, 4291-4340.

  8. K. Coulembier, On a class of tensor product representations for orthosymplectic superalgebras. J. Pure Appl. Algebra 217 (2013), 819-837.

  9. K. Coulembier, The orthosymplectic superalgebra in harmonic analysis. J. Lie Theory 23 (2013) 55-83.

  10. K. Coulembier and R.B. Zhang, Invariant integration on orthosymplectic and unitary supergroups. J. Phys. A: Math. Theor. 45 (2012) 095204 (36 pp).

  11. K. Coulembier and H. De Bie, Hilbert space for quantum mechanics on superspace. J. Math. Phys. 52 (2011) 063504 (30 pp).

  12. K. Coulembier, The Fourier transform on quantum Euclidean space. SIGMA 7 (2011), 047 (30pp).

  13. K. Coulembier, H. De Bie and F. Sommen, Orthogonality of the Hermite functions in superspace and Mehler type formulae. Proc. London Math. Soc. 103 (2011), 786-825.

  14. K. Coulembier and F. Sommen, Operator identities in q-deformed Clifford analysis. Adv. appl. Clifford alg. 21 (2011), 677-696.

  15. K. Coulembier, H. De Bie and F. Sommen, Orthosymplectically invariant functions in superspace. J. Math. Phys. 51 (2010) 083504 (23pp).

  16. K. Coulembier and F. Sommen, q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials. J. Phys. A: Math. Theor. 43 (2010) 115202 (28pp).

  17. K. Coulembier, H. De Bie and F. Sommen, Integration in superspace using distribution theory. J. Phys. A: Math. Theor. 42 (2009) 395206 (23pp).

P1-papers

  1. K. Coulembier, Homological algebra for osp(1|2n). Accepted in: Gorelik, M.; Papi. P. (Eds.) Springer INdAM Series.

  2. K. Coulembier, The orthosymplectic Lie supergroup in harmonic analysis. AIP Conf. Proc. -- September 30, 2010 -- Volume 1281, pp. 1459-1463 ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010

  3. K. Coulembier, H. De Bie and F. Sommen, Harmonic and monogenic functions in superspace. In ''Hypercomplex Analysis and Applications'', Trends in Mathematics, Birkhauser, pp. 29-41.