Published paper
- Marked chain-order polytopes and string polytopes, with X.Fang, European J. of Combinatorics, DOI 10.1016/j.ejc.2016.06.007
- 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.
- Torus fixed points in Schubert varieties and Genocchi numbers, with X.Fang, Seminaire Lotharingien de Combinatoire 75 (2016), Article B75f
- PBW-degenerated Demazure modules and Schubert varieties for triangular elements, Journal of Combinatorial Theory, Series A, Volume 139, April 2016, Pages 132-152.
- Favourable modules: Filtrations, polytopes, Newton-Okounkov
bodies and flat degenerations, with E.Feigin and P.Littelmann, Transformation Groups, DOI 10.1007/s00031-016-9389-2, 2016.
- Marked poset polytopes: Minkowski sums, indecomposables, and
unimodular equivalence, Journal of Pure and Applied Algebra, 220 (2), pp. 606-620, 2016
- 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
- New homogeneous ideals for current algebras: filtrations,
fusion products, and the Pieri rules, Moscow Mathematical Journal, Volume 15 (1), 2015 pp. 49-72.
- 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.
- Schur positivity and Kirillov-Reshetikhin modules, with
D.Hernandez, SIGMA 10 (2014).
- Global Weyl modules for equivariant map algebras, with N.Manning
and A.Savage, International Mathematics Research Notices, 2014;
doi: 10.1093/imrn/rnt231
- Weyl modules and Levi subalgebras, Journal of Lie Theory, 24,
(2014), No. 2, 503-527.
- Extended partial order and applications to tensor products, Australasian
J. of Combinatorics 58(1), 178-196, (2014).
- 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.
- 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
- 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.
- 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
- Demazure and Weyl modules: The twisted current case, with D.Kus, Transactions
of the AMS, Volume 365, p. 6037-6064 (2013).
- 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) .
- PBW filtration and bases for symplectic Lie algebras, with
E.Feigin and P.Littelmann, International
Mathematics Research
Notices, first published online February 17, (2011).
- 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.
- A categorical approach to Weyl modules, with V.Chari and
T.Khandai, Transform. Groups 15, no. 3, 517-549, (2010) .
- 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).
- Kirillov-Reshetikhin modules of non-exceptionel type, with
M.Okado and A.Schilling, Advances in Mathematics, Volume 222, p.
1080-1116, (2009).
- Weyl modules for twisted loop algebras, with V.Chari and
P.Senesi, Journal
of Algebra, Volume 319, p.5016-5038, (2008).
- Demazure structure inside Kirillov-Reshetikhin crystals, with
A.Schilling and M.Shimozono, Journal of Algebra, Volume 309, p.
386-404, (2007).
- Weyl modules, Demazure modules, KR-modules, crystals, fusion
products and limit constructions, with P.Littelmann, Advances in
Mathematics, Volume 211, p. 566-593, (2007).
- Tensor product structure of affine Demazure modules and limit
constructions, with P.Littelmann, Nagoya Math. Journal., Vol. 182,
p. 171-198, (2006).
Preprints
- On toric degenerations of flag varieties, with X.Fang and P.Littelmann, preprint
- Linear degenerations of flag varieties, with G.Cerulli Irelli, E.Feigin, X.Fang and M.Reineke, arXiv:1603.08395
- Degree cones and monomial bases of Lie algebras and quantum groups, with T.Backhaus and X.Fang, arXiv:1605.00417
- Essential bases and toric degenerations arising from birational sequences, with X.Fang and P.Littelmann, arXiv:1510.02295
Theses
- Finite-dimensional modules of generalized current algebras: KR
crystals, PBW filtrations and Weyl modules, Habilitation, Januar
2013.
- Some results on finite dimensional modules of current and loop
algebras, Dissertation, Oktober 2007.
- Tensor product factorization of affine Demazure modules,
Diplomarbeit, September 2004.
Slides of recent presentations
- Annual conference of the DFG priority program "Representation Theory" in Bad Honnef, Germany, 09.March 2015
- Workshop at the Hausdorff Institute for Mathematics in Bonn, Germany, 30.March 2015