Publications

Papers & preprints

1. 2026
   The Hibi-Li Face-Number Conjecture

   Preprint · arXiv:2609.23629
2. 2026
   Makhlin polytopes are Demazure string polytopes

   Preprint · arXiv:2608.23431
3. 2026
   On facet gaps of order and chain polytopes

   Preprint · arXiv:2608.19989
4. 2026
   Order and chain polytopes of maximal ranked posets — with I. Ahmad, M. Joswig

   Discrete Applied Mathematics 390, 28–39. arXiv
5. 2026
   Specialization map for quiver Grassmannians — with G. C. Irelli, F. Esposito, X. Fang

   Algebras and Representation Theory, published online 9 May 2026. arXiv
6. 2026
   KI-Tutor im Online-Mathematik-Brückenkurs OMB+ — with V. Bach, I. Gasser, A. Krieg, R. Seiler

   Mitteilungen der Deutschen Mathematiker-Vereinigung 34(3), 166–171
7. 2025
   The Real Vanishing Ideals of Nuclear p-Norm Balls — with Y. Zhou

   Preprint · arXiv:2510.24661
8. 2025
   Monomial Bases in Lie Theory — with X. Fang

   The Computer Algebra System OSCAR: Algorithms and Examples, Algorithms and Computation in Mathematics 32, 333–349
9. 2024
   Linear degenerate symplectic flag varieties: symmetric degenerations and PBW locus — with M. Boos, G. C. Irelli, X. Fang

   Preprint · arXiv:2405.02739
10. 2024
    Dynkin abelianisations of flag varieties — with S. V. Enugandla, X. Fang, C. Steinert

    Preprint · arXiv:2404.05277
11. 2024
    Computing monomial bases in Lie theory using OSCAR — with X. Fang, L. Göttgens, B. Wilop

    Preprint · arXiv:2403.15018
12. 2024
    FFLV polytopes are string polytopes — with E. Cleusters, F. Lerner

    Preprint · arXiv:2402.01492
13. 2024
    A minimal Gröbner basis for simple slₙ- or spₙ-modules — with L. v. Eß

    Preprint · arXiv:2401.01634
14. 2023
    PBW filtration and monomial bases for Demazure modules in types A and C — with G. Balla, K. Kambaso

    Beiträge zur Algebra und Geometrie 64, 887–907. arXiv
15. 2023
    Gröbner bases for fusion products — with J. Flake, V. Levandovskyy

    Algebras and Representation Theory 26, 2235–2253. arXiv
16. 2023
    Degenerate flag varieties in network coding — with G. Nebe

    Advances in Mathematics of Communications 17(4), 888–899. arXiv
17. 2021
    Cones from quantum groups to tropical flag varieties — with X. Fang, M. Reineke

    Journal of Algebraic Combinatorics 54, 815–835. arXiv
18. 2021
    PBW degenerations of Lie superalgebras and their typical representations — with D. Kus

    Journal of Lie Theory 31(2), 313–334. arXiv
19. 2021
    Degenerate Schubert Varieties in Type A — with R. Chirivì, X. Fang

    Transformation Groups 26, 1189–1215. arXiv
20. 2020
    Linear degenerations of flag varieties: partial flags, defining equations, and group actions — with G. C. Irelli, X. Fang, E. Feigin, M. Reineke

    Mathematische Zeitschrift 296, 453–477. arXiv
21. 2020
    The Minkowski Property and Reflexivity of Marked Poset Polytopes — with X. Fang, C. Pegel

    The Electronic Journal of Combinatorics 27(1), P1.27. arXiv
22. 2020
    A Continuous Family of Marked Poset Polytopes — with X. Fang, J. Litza, C. Pegel

    SIAM Journal on Discrete Mathematics 34(1), 611–639. arXiv
23. 2019
    On Truncated Weyl Modules — with V. Martins, A. Moura

    Communications in Algebra. arXiv
24. 2019
    Weighted PBW degenerations and tropical flag varieties — with X. Fang, E. Feigin, I. Makhlin

    Communications in Contemporary Mathematics 21(1), 1850016. arXiv
25. 2019
    String cone and Superpotential combinatorics for flag and Schubert varieties in type A — with L. Bossinger

    Journal of Combinatorial Theory, Series A 167, 213–256. arXiv
26. 2018
    Symmetries on plabic graphs and associated polytopes — with X. Fang

    Comptes Rendus Mathématique 356(6), 581–585. arXiv
27. 2018
    Toric degenerations of Gr(2,n) and Gr(3,6) via plabic graphs — with L. Bossinger, X. Fang, M. Hering, M. Lanini

    Annals of Combinatorics 22, 491–512. arXiv
28. 2017
    On toric degenerations of flag varieties — with X. Fang, P. Littelmann

    European Mathematical Society, survey contribution. arXiv
29. 2017
    Degree cones and monomial bases of Lie algebras and quantum groups — with T. Backhaus, X. Fang

    Glasgow Mathematical Journal 59(3), 595–621. arXiv
30. 2017
    Linear degenerations of flag varieties — with G. C. Irelli, X. Fang, E. Feigin, M. Reineke

    Mathematische Zeitschrift 287, 615–654. arXiv
31. 2017
    Essential bases and toric degenerations arising from birational sequences — with X. Fang, P. Littelmann

    Advances in Mathematics 312, 107–149. arXiv
32. 2017
    Favourable modules: Filtrations, polytopes, Newton-Okounkov bodies and flat degenerations — with E. Feigin, P. Littelmann

    Transformation Groups 22(2), 321–352. arXiv
33. 2016
    Marked chain-order polytopes — with X. Fang

    European Journal of Combinatorics 58, 267–282. arXiv
34. 2016
    Torus fixed points in Schubert varieties and normalized median Genocchi numbers — with X. Fang

    Séminaire Lotharingien de Combinatoire 75, Article B75f. arXiv
35. 2016
    PBW-type filtration on quantum groups of type Aₙ — with X. Fang, M. Reineke

    Journal of Algebra 449, 321–345. arXiv
36. 2016
    Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence

    Journal of Pure and Applied Algebra 220(2), 606–620. arXiv
37. 2016
    PBW-degenerated Demazure modules and Schubert varieties for triangular elements

    Journal of Combinatorial Theory, Series A 139, 132–152. arXiv
38. 2015
    Minuscule Schubert varieties: Poset polytopes, PBW-degenerated Demazure modules, and Kogan faces — with R. Biswal

    Algebras and Representation Theory 18(6), 1481–1503. arXiv
39. 2015
    New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules

    Moscow Mathematical Journal 15(1), 49–72. arXiv
40. 2015
    Global Weyl modules for equivariant map algebras — with N. Manning, A. Savage

    International Mathematics Research Notices 2015(7), 1794–1847. arXiv
41. 2014
    The degree of the Hilbert-Poincaré polynomial of PBW-graded modules — with T. Backhaus, L. Bossinger, C. Desczyk

    Comptes Rendus Mathématique 352(12), 959–963. arXiv
42. 2014
    Schur Positivity and Kirillov-Reshetikhin Modules — with D. Hernandez

    SIGMA 10, 058. arXiv
43. 2014
    Weyl modules and Levi subalgebras

    Journal of Lie Theory 24(2), 503–527. arXiv
44. 2014
    Extended partial order and applications to tensor products

    Australasian Journal of Combinatorics 58(1), 178–196. arXiv
45. 2014
    Posets, Tensor Products and Schur positivity — with V. Chari, D. Sagaki

    Algebra & Number Theory 8(4), 933–961. arXiv
46. 2014
    On multigraded generalizations of Kirillov-Reshetikhin modules — with A. Bianchi, V. Chari, A. Moura

    Algebras and Representation Theory 17(2), 519–538. arXiv
47. 2013
    PBW-filtration over ℤ and compatible bases for Vℤ(λ) in type Aₙ and Cₙ — with E. Feigin, P. Littelmann

    Symmetries, Integrable Systems and Representations, Springer Proceedings in Mathematics & Statistics 40, 35–63. arXiv
48. 2013
    Global Weyl modules for the twisted loop algebra — with N. Manning, P. Senesi

    Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 83(1), 53–82. arXiv
49. 2013
    Demazure modules and Weyl modules: The twisted current case — with D. Kus

    Transactions of the American Mathematical Society 365(11), 6037–6064. arXiv
50. 2012
    Local Weyl modules for equivariant map algebras with free abelian group actions — with T. Khandai, D. Kus, A. Savage

    Journal of Algebra 350, 386–404. arXiv
51. 2011
    PBW filtration and bases for symplectic Lie algebras — with E. Feigin, P. Littelmann

    International Mathematics Research Notices 2011(24), 5760–5784. arXiv
52. 2011
    PBW filtration and bases for irreducible modules in type Aₙ — with E. Feigin, P. Littelmann

    Transformation Groups 16(1), 71–89. arXiv
53. 2010
    A categorical approach to Weyl modules — with V. Chari, T. Khandai

    Transformation Groups 15(3), 517–549. arXiv
54. 2010
    Perfectness of Kirillov-Reshetikhin crystals for nonexceptional types — with M. Okado, A. Schilling

    Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications, Contemporary Mathematics 506, 127–143. arXiv
55. 2009
    Kirillov–Reshetikhin crystals for nonexceptional types — with M. Okado, A. Schilling

    Advances in Mathematics 222, 1080–1116. arXiv
56. 2008
    Weyl modules for the twisted loop algebras — with V. Chari, P. Senesi

    Journal of Algebra 319(12), 5016–5038. arXiv
57. 2007
    Demazure structure inside Kirillov-Reshetikhin crystals — with A. Schilling, M. Shimozono

    Journal of Algebra 309, 386–404. arXiv
58. 2007
    Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions — with P. Littelmann

    Advances in Mathematics 211(2), 566–593. arXiv
59. 2006
    Tensor product structure of affine Demazure modules and limit constructions — with P. Littelmann

    Nagoya Mathematical Journal 182, 171–198. arXiv

Book

Aspekte der Mathematik

Ghislain Fourier, Verity Mackscheidt and Petra Schwer

A book for discovering mathematics and the connections between its different areas.

Book at Springer