Logo Leibniz Universität Hannover
Institut für
Algebra, Zahlentheorie und Diskrete Mathematik
Logo Leibniz Universität Hannover
Institut für
Algebra, Zahlentheorie und Diskrete Mathematik
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Published paper

  1. Toric degenerations of Gr(2,n) and Gr(3,6) via plabic graphs, with L.Bossinger, X.Fang, M.Hering and M.Lanini, Annals of Combinatorics, https://doi.org/10.1007/s00026-018-0395-z, arXiv:1612.03838
  2. Weighted PBW degenerations and tropical flag varieties, with X.Fang, E.Feigin and I.Makhlin, to appear in Communications in Contemporary Mathematics, arXiv:1711.00751
  3. Fang, Xin; Fourier, Ghislain; Symmetries on plabic graphs and associated polytopes. C.R. Math. Acad. Sci. Paris 356 (2018), no. 6, 581-585.
  4. On truncated Weyl modules, with V.Martins and A.Moura, to appear in Communications in Algebra, arXiv:1711.09631
  5. Essential bases and toric degenerations arising from birational sequences, with X.Fang and P.Littelmann, Advances in Mathematics, 312, 2017, pp 107-149
  6. Linear degenerations of flag varieties, with G.Cerulli Irelli, X.Fang, E.Feigin, M.Reineke, Mathematische Zeitschrift 287 (2017).no 1-2, 615-654  doi:10.1007/s00209-016-1839-y
  7. On toric degenerations of flag varieties, with X.Fang and P.Littelmann, Representation Theory - Current Trends and Perspectives, EMS - Series of Congress Reports, 2017, p.187--232.
  8. Degree cones and monomial bases of Lie algebras and quantum groups, with T.Backhaus and X.Fang, Glasgow Mathematical Journal 59 (2018), no. 3, 595-621. doi:10.1017/S0017089516000422
  9. Marked chain-order polytopes, with X.Fang, European J. of Combinatorics 58 (2016), 267-282. doi:10.1016/j.ejc.2016.06.007.
  10. PBW type filtration for quantum groups of type A_n, with X.Fang and M.Reineke, Journal of Algebra, Volume 449 (1), pp 321-345, 2016.
  11. Torus fixed points in Schubert varieties and Genocchi numbers, with X.Fang, Seminaire Lotharingien de Combinatoire 75 (2016), Article B75f
  12. PBW-degenerated Demazure modules and Schubert varieties for triangular elements, Journal of Combinatorial Theory, Series A, Volume 139, April 2016, Pages 132-152.
  13. Favourable modules: Filtrations, polytopes, Newton-Okounkov bodies and flat degenerations, with E.Feigin and P.Littelmann, Transformation Groups, 2017, 22-2, pp 321–352
  14. Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence, Journal of Pure and Applied Algebra, 220 (2), pp. 606-620, 2016
  15. Minuscule Schubert varieties: Poset polytopes, PBW-degenerated Demazure modules, and Kogan faces, with R.Biswal, Algebras and Representation Theory, DOI 10.1007/s10468-015-9548-5, 2015
  16. New homogeneous ideals for current algebras: filtrations, fusion products, and the Pieri rules, Moscow Mathematical Journal, Volume 15 (1), 2015 pp. 49-72.
  17. The degree of the Hilbert-Poincare polynomial of PBW-graded modules, with T.Backhaus, L.Bossinger and C.Desczyk, C. R. Math. Acad. Sci. Paris 352 (2014), no. 12, 959-963.
  18. Schur positivity and Kirillov-Reshetikhin modules, with D.Hernandez, SIGMA 10 (2014).
  19. Global Weyl modules for equivariant map algebras, with N.Manning and A.Savage, International Mathematics Research Notices, 2014; doi: 10.1093/imrn/rnt231
  20. Weyl modules and Levi subalgebras, Journal of Lie Theory, 24, (2014), No. 2, 503-527.
  21. Extended partial order and applications to tensor products, Australasian J. of Combinatorics 58(1), 178-196, (2014).
  22. Posets, tensor products and Schur positivity, with V.Chari and D.Sagaki, Algebra and Number Theory 8-4 (2014), 933--961. DOI 10.2140/ant.2014.8.933.
  23. On multigraded generalizations of Kirillov-Reshetikhin modules, with A.Bianchi, V.Chari and A.Moura, Algebras and Representation Theory, 2013, 10.1007/s10468-013-9408-0
  24. PBW filtration over Z and compatible bases for simple modules in type A_n and C_n, with E.Feigin and P.Littelmann, Symmetries, Integrable Systems and Representations, Springer Proceedings in Mathematics and Statistics 40.
  25. Global Weyl modules for the twisted loop algebra, with N.Manning and P.Senesi, Abhandlungen a.d. Math. Sem. d. Univ. Hamburg, Volume 83, 1, p.53-82, 2013
  26. Demazure and Weyl modules: The twisted current case, with D.Kus, Transactions of the AMS, Volume 365, p. 6037-6064 (2013).
  27. Local Weyl modules for equivariant map algebras with free abelian group actions, with T.Khandai, D.Kus and A.Savage, Journal of Algebra, Volume 350, p.386-404, (2012) .
  28. PBW filtration and bases for symplectic Lie algebras, with E.Feigin and P.Littelmann, International Mathematics Research Notices, first published online February 17, (2011).
  29. PBW filtration and bases for irreducible modules in type A_n, with E.Feigin and P.Littelmann, Transform. Groups 16 (2011), no. 1, 71-89.
  30. A categorical approach to Weyl modules, with V.Chari and T.Khandai, Transform. Groups 15, no. 3, 517-549, (2010) .
  31. Perfectness of Kirillov-Reshetikhin modules of non-exceptionel type, with M.Okado and A.Schilling, Quantum affine algebras, extended affine Lie algebras, and their applications, 127--143, Contemp. Math., 506, AMS, (2010).
  32. Kirillov-Reshetikhin modules of non-exceptionel type, with M.Okado and A.Schilling, Advances in Mathematics, Volume 222, p. 1080-1116, (2009).
  33. Weyl modules for twisted loop algebras, with V.Chari and P.Senesi, Journal of Algebra, Volume 319, p.5016-5038, (2008).
  34. Demazure structure inside Kirillov-Reshetikhin crystals, with A.Schilling and M.Shimozono, Journal of Algebra, Volume 309, p. 386-404, (2007).
  35. Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions, with P.Littelmann, Advances in Mathematics, Volume 211, p. 566-593, (2007).
  36. Tensor product structure of affine Demazure modules and limit constructions, with P.Littelmann, Nagoya Math. Journal., Vol. 182, p. 171-198, (2006).

Preprints

  1. String cone and Superpotential combinatorics for flag and Schubert varieties in type A, with L.Bossinger, arXiv:1611.06504
  2. A continuous family of marked poset polytopes, with X.Fang, J.-P- Litza and C.Pegel, arxiv:1712.01037
  3. The Minkowski Property and Reflexivity of Marked Poset Polytopes, with X.Fang and C.Pegel, arxiv:1807.03970

Theses

  1. Finite-dimensional modules of generalized current algebras: KR crystals, PBW filtrations and Weyl modules, Habilitation, Januar 2013.
  2. Some results on finite dimensional modules of current and loop algebras, Dissertation, Oktober 2007.
  3. Tensor product factorization of affine Demazure modules, Diplomarbeit, September 2004.