Dr Ghislain Fourier

  • Honorary Research Fellow (School of Mathematics & Statistics)

email: Ghislain.Fourier@glasgow.ac.uk

Mathematics Building

Publications

List by: Type | Date

Jump to: 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006
Number of items: 32.

2017

Cerulli Irelli, G., Fang, X., Feigin, E., Fourier, G. and Reineke, M. (2017) Linear degenerations of flag varieties. Mathematische Zeitschrift, 287(1-2), pp. 615-654. (doi: 10.1007/s00209-016-1839-y)

Feigin, E., Fourier, G. and Littelmann, P. (2017) Favourable modules: filtrations, polytopes, Newton-Okounkov bodies and flat degenerations. Transformation Groups, 22(2), pp. 321-352. (doi: 10.1007/s00031-016-9389-2)

Fang, X., Fourier, G. and Littelmann, P. (2017) Essential bases and toric degenerations arising from birational sequences. Advances in Mathematics, 312, pp. 107-149. (doi: 10.1016/j.aim.2017.03.014)

Fang, X., Fourier, G. and Littelmann, P. (2017) On toric degenerations of flag varieties. In: Krause, H., Littlemann, P., Malle, G., Neeb, K.-H. and Schweigert, C. (eds.) Representation Theory: Current Trends and Perspectives. Series: EMS series of congress reports. European Mathematical Society: Zürich, Switzerland, pp. 187-232. ISBN 9783037191712 (doi:10.4171/171-1/8)

2016

Fang, X. and Fourier, G. (2016) Marked chain-order polytopes. European Journal of Combinatorics, 58, pp. 267-282. (doi: 10.1016/j.ejc.2016.06.007)

Fourier, G. (2016) PBW-degenerated Demazure modules and Schubert varieties for triangular elements. Journal of Combinatorial Theory, Series A, 139, pp. 132-152. (doi: 10.1016/j.jcta.2015.12.001)

Fang, X., Fourier, G. and Reineke, M. (2016) PBW-type filtration on quantum groups of type An. Journal of Algebra, 449, pp. 321-345. (doi: 10.1016/j.jalgebra.2015.09.054)

Fourier, G. (2016) Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence. Journal of Pure and Applied Algebra, 220(2), pp. 606-620. (doi: 10.1016/j.jpaa.2015.07.007)

Fang, X. and Fourier, G. (2016) Torus fixed points in Schubert varieties and Genocchi numbers. Séminaire Lotharingien de Combinatoire, 75, B75f.

2015

Fourier, G. and Biswal, R. (2015) Minuscule Schubert varieties: poset polytopes, PBW-degenerated demazure modules, and Kogan faces. Algebras and Representation Theory, 18(6), pp. 1481-1503. (doi: 10.1007/s10468-015-9548-5)

Fourier, G. (2015) New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules. Moscow Mathematical Journal, 15(1), pp. 49-72.

2014

Backhaus, T., Desczyk, C., Bossinger, L. and Fourier, G. (2014) The degree of the Hilbert–Poincaré polynomial of PBW-graded modules. Comptes Rendus Mathématique, 352(12), pp. 959-963. (doi: 10.1016/j.crma.2014.09.027)

Bianchi, A., Chari, V., Fourier, G. and Moura, A. (2014) On multigraded generalizations of Kirillov-Reshetikhin modules. Algebras and Representation Theory, 17(2), pp. 519-538. (doi: 10.1007/s10468-013-9408-0)

Chari, V., Fourier, G. and Sagaki, D. (2014) Posets, tensor products and Schur positivity. Algebra and Number Theory, 8(4), pp. 933-961. (doi: 10.2140/ant.2014.8.933)

Fourier, G. (2014) Extended partial order and applications to tensor products. Australasian Journal of Combinatorics, 58, pp. 178-196.

Fourier, G. (2014) PBW-degenerated Demazure modules and Schubert varieties for triangular elements. arXiv, (Unpublished)

Fourier, G. (2014) Weyl modules and Levi subalgebras. Journal of Lie Theory, 24(2), pp. 503-527.

Fourier, G. and Hernandez, D. (2014) Schur positivity and Kirillov-Reshetikhin modules. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 10(058), (doi: 10.3842/SIGMA.2014.058)

2013

Fourier, G., Savage, A. and Manning, N. (2013) Global Weyl modules for equivariant map algebras. International Mathematics Research Notices, (Unpublished)

Fourier, G., Manning, N. and Senesi, P. (2013) Global Weyl modules for the twisted loop algebra. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 83(1), pp. 53-82. (doi: 10.1007/s12188-013-0074-2)

Feigin, E., Fourier, G. and Littelmann, P. (2013) PBW-filtration over ℤ and compatible bases for V(λ) in type An and Cn. In: Symmetries, Integrable Systems and Representations, Université Claude Bernard Lyon 1, Lyon, France, 13-16 Dec 2011, pp. 35-63. (doi:10.1007/978-1-4471-4863-0_3)

Fourier, G. and Kus, D. (2013) Demazure modules and Weyl modules: the twisted current case. Transactions of the American Mathematical Society, 365, pp. 6037-6064. (doi: 10.1090/S0002-9947-2013-05846-1)

2012

Fourier, G., Khandai, T., Kus, D. and Savage, A. (2012) Local Weyl modules for equivariant map algebras with free abelian group actions. Journal of Algebra, 350(1), pp. 386-404. (doi: 10.1016/j.jalgebra.2011.10.018)

2011

Feigin, E., Fourier, G. and Littelmann, P. (2011) PBW filtration and bases for irreducible modules in type An. Transformation Groups, 16(1), pp. 71-89. (doi: 10.1007/s00031-010-9115-4)

Feigin, E., Fourier, G. and Littelmann, P. (2011) PBW filtration and bases for symplectic Lie algebras. International Mathematics Research Notices, 2011(24), pp. 5760-5784. (doi: 10.1093/imrn/rnr014)

2010

Chari, V., Fourier, G. and Khandai, T. (2010) A categorical approach to Weyl modules. Transformation Groups, 15(3), pp. 517-549. (doi: 10.1007/s00031-010-9090-9)

Fourier, G., Okado, M. and Schilling, A. (2010) Perfectness of Kirillov-Reshetikhin crystals for nonexceptional types. In: Gao, Y., Jing, N., Lau, M. and Misra, K. C. (eds.) Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications. Series: Contemporary mathematics, 506 (506). American Mathematical Society: Providence, RI, pp. 127-143. ISBN 9780821845073 (doi:10.1090/conm/506/09938)

2009

Fourier, G., Okado, M. and Schilling, A. (2009) Kirillov-reshetikhin crystals for nonexceptional types. Advances in Mathematics, 222(3), pp. 1080-1116. (doi: 10.1016/j.aim.2009.05.020)

2008

Chari, V., Fourier, G. and Senesi, P. (2008) Weyl modules for the twisted loop algebras. Journal of Algebra, 319(12), pp. 5016-5038. (doi: 10.1016/j.jalgebra.2008.02.030)

2007

Fourier, G. and Littelmann, P. (2007) Weyl modules, demazure modules, KR-modules, crystals, fusion products and limit constructions. Advances in Mathematics, 211(2), pp. 566-593. (doi: 10.1016/j.aim.2006.09.002)

Fourier, G., Schilling, A. and Shimozono, M. (2007) Demazure structure inside Kirillov-Reshetikhin crystals. Journal of Algebra, 309(1), pp. 386-404. (doi: 10.1016/j.jalgebra.2006.09.019)

2006

Fourier, G. and Littelmann, P. (2006) Tensor product structure of affine Demazure modules and limit constructions. Nagoya Mathematical Journal, 182, pp. 171-198.

This list was generated on Mon Sep 20 21:08:30 2021 BST.
Number of items: 32.

Articles

Cerulli Irelli, G., Fang, X., Feigin, E., Fourier, G. and Reineke, M. (2017) Linear degenerations of flag varieties. Mathematische Zeitschrift, 287(1-2), pp. 615-654. (doi: 10.1007/s00209-016-1839-y)

Feigin, E., Fourier, G. and Littelmann, P. (2017) Favourable modules: filtrations, polytopes, Newton-Okounkov bodies and flat degenerations. Transformation Groups, 22(2), pp. 321-352. (doi: 10.1007/s00031-016-9389-2)

Fang, X., Fourier, G. and Littelmann, P. (2017) Essential bases and toric degenerations arising from birational sequences. Advances in Mathematics, 312, pp. 107-149. (doi: 10.1016/j.aim.2017.03.014)

Fang, X. and Fourier, G. (2016) Marked chain-order polytopes. European Journal of Combinatorics, 58, pp. 267-282. (doi: 10.1016/j.ejc.2016.06.007)

Fourier, G. (2016) PBW-degenerated Demazure modules and Schubert varieties for triangular elements. Journal of Combinatorial Theory, Series A, 139, pp. 132-152. (doi: 10.1016/j.jcta.2015.12.001)

Fang, X., Fourier, G. and Reineke, M. (2016) PBW-type filtration on quantum groups of type An. Journal of Algebra, 449, pp. 321-345. (doi: 10.1016/j.jalgebra.2015.09.054)

Fourier, G. (2016) Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence. Journal of Pure and Applied Algebra, 220(2), pp. 606-620. (doi: 10.1016/j.jpaa.2015.07.007)

Fang, X. and Fourier, G. (2016) Torus fixed points in Schubert varieties and Genocchi numbers. Séminaire Lotharingien de Combinatoire, 75, B75f.

Fourier, G. and Biswal, R. (2015) Minuscule Schubert varieties: poset polytopes, PBW-degenerated demazure modules, and Kogan faces. Algebras and Representation Theory, 18(6), pp. 1481-1503. (doi: 10.1007/s10468-015-9548-5)

Fourier, G. (2015) New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules. Moscow Mathematical Journal, 15(1), pp. 49-72.

Backhaus, T., Desczyk, C., Bossinger, L. and Fourier, G. (2014) The degree of the Hilbert–Poincaré polynomial of PBW-graded modules. Comptes Rendus Mathématique, 352(12), pp. 959-963. (doi: 10.1016/j.crma.2014.09.027)

Bianchi, A., Chari, V., Fourier, G. and Moura, A. (2014) On multigraded generalizations of Kirillov-Reshetikhin modules. Algebras and Representation Theory, 17(2), pp. 519-538. (doi: 10.1007/s10468-013-9408-0)

Chari, V., Fourier, G. and Sagaki, D. (2014) Posets, tensor products and Schur positivity. Algebra and Number Theory, 8(4), pp. 933-961. (doi: 10.2140/ant.2014.8.933)

Fourier, G. (2014) Extended partial order and applications to tensor products. Australasian Journal of Combinatorics, 58, pp. 178-196.

Fourier, G. (2014) PBW-degenerated Demazure modules and Schubert varieties for triangular elements. arXiv, (Unpublished)

Fourier, G. (2014) Weyl modules and Levi subalgebras. Journal of Lie Theory, 24(2), pp. 503-527.

Fourier, G. and Hernandez, D. (2014) Schur positivity and Kirillov-Reshetikhin modules. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 10(058), (doi: 10.3842/SIGMA.2014.058)

Fourier, G., Savage, A. and Manning, N. (2013) Global Weyl modules for equivariant map algebras. International Mathematics Research Notices, (Unpublished)

Fourier, G., Manning, N. and Senesi, P. (2013) Global Weyl modules for the twisted loop algebra. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 83(1), pp. 53-82. (doi: 10.1007/s12188-013-0074-2)

Fourier, G. and Kus, D. (2013) Demazure modules and Weyl modules: the twisted current case. Transactions of the American Mathematical Society, 365, pp. 6037-6064. (doi: 10.1090/S0002-9947-2013-05846-1)

Fourier, G., Khandai, T., Kus, D. and Savage, A. (2012) Local Weyl modules for equivariant map algebras with free abelian group actions. Journal of Algebra, 350(1), pp. 386-404. (doi: 10.1016/j.jalgebra.2011.10.018)

Feigin, E., Fourier, G. and Littelmann, P. (2011) PBW filtration and bases for irreducible modules in type An. Transformation Groups, 16(1), pp. 71-89. (doi: 10.1007/s00031-010-9115-4)

Feigin, E., Fourier, G. and Littelmann, P. (2011) PBW filtration and bases for symplectic Lie algebras. International Mathematics Research Notices, 2011(24), pp. 5760-5784. (doi: 10.1093/imrn/rnr014)

Chari, V., Fourier, G. and Khandai, T. (2010) A categorical approach to Weyl modules. Transformation Groups, 15(3), pp. 517-549. (doi: 10.1007/s00031-010-9090-9)

Fourier, G., Okado, M. and Schilling, A. (2009) Kirillov-reshetikhin crystals for nonexceptional types. Advances in Mathematics, 222(3), pp. 1080-1116. (doi: 10.1016/j.aim.2009.05.020)

Chari, V., Fourier, G. and Senesi, P. (2008) Weyl modules for the twisted loop algebras. Journal of Algebra, 319(12), pp. 5016-5038. (doi: 10.1016/j.jalgebra.2008.02.030)

Fourier, G. and Littelmann, P. (2007) Weyl modules, demazure modules, KR-modules, crystals, fusion products and limit constructions. Advances in Mathematics, 211(2), pp. 566-593. (doi: 10.1016/j.aim.2006.09.002)

Fourier, G., Schilling, A. and Shimozono, M. (2007) Demazure structure inside Kirillov-Reshetikhin crystals. Journal of Algebra, 309(1), pp. 386-404. (doi: 10.1016/j.jalgebra.2006.09.019)

Fourier, G. and Littelmann, P. (2006) Tensor product structure of affine Demazure modules and limit constructions. Nagoya Mathematical Journal, 182, pp. 171-198.

Book Sections

Fang, X., Fourier, G. and Littelmann, P. (2017) On toric degenerations of flag varieties. In: Krause, H., Littlemann, P., Malle, G., Neeb, K.-H. and Schweigert, C. (eds.) Representation Theory: Current Trends and Perspectives. Series: EMS series of congress reports. European Mathematical Society: Zürich, Switzerland, pp. 187-232. ISBN 9783037191712 (doi:10.4171/171-1/8)

Fourier, G., Okado, M. and Schilling, A. (2010) Perfectness of Kirillov-Reshetikhin crystals for nonexceptional types. In: Gao, Y., Jing, N., Lau, M. and Misra, K. C. (eds.) Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications. Series: Contemporary mathematics, 506 (506). American Mathematical Society: Providence, RI, pp. 127-143. ISBN 9780821845073 (doi:10.1090/conm/506/09938)

Conference Proceedings

Feigin, E., Fourier, G. and Littelmann, P. (2013) PBW-filtration over ℤ and compatible bases for V(λ) in type An and Cn. In: Symmetries, Integrable Systems and Representations, Université Claude Bernard Lyon 1, Lyon, France, 13-16 Dec 2011, pp. 35-63. (doi:10.1007/978-1-4471-4863-0_3)

This list was generated on Mon Sep 20 21:08:30 2021 BST.