Photo of Peter  Fiebig

Prof. Dr. Peter Fiebig

Department Mathematik
Emmy-Noether-Zentrum
FAU Erlangen-Nürnberg
Cauerstr. 11
91058 Erlangen

Room: 01.319

Email: fiebig@mi.uni-erlangen.de
Phone: +49 9131 85-67018
Fax: +49 9131 85-67020
Office hours: jederzeit nach Vereinbarung

Arbeitsgebiet

Arbeitsgruppe

Preprints und Veröffentlichungen

  • Moment graphs in representation theory and geometry, preprint 2013, arXiv:1308.2873, eingereicht.
  • On the subgeneric restricted blocks of affine category O at the critical level, preprint 2012, arXiv:1206.0683, in "Symmetries, Integrable Systems and Representations", Springer Proceedings in Mathematics and Statistics 40 (2013), 65-84.
  • On the restricted projective objects in the affine category O at the critical level, preprint 2011, arXiv:1103.1540, in "Algebraic Groups and Quantum Groups" (Nagoya, Japan, 2010),  Contemp. Math. 565 (2012), 55-70.
  • (mit Geordie Williamson) Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties, preprint 2010, arXiv:1008.0719, erscheint in Ann. Inst. Fourier.
  • (mit Tomoyuki Arakawa) The linkage principle for restricted critical level representations of affine Kac-Moody algebras, preprint 2009, arXiv:0909.4214, Compos. Math. 148 (2012), 1787-1810.
  • (mit Tomoyuki Arakawa) On the restricted Verma modules at the critical level, preprint 2008, arXiv:0812.3334, Trans. Amer. Math. Soc. 364 (2012), 4683-4712.
  • An upper bound on the exceptional characteristics for Lusztig's character formula, preprint 2008, arXiv:0811.1674, J. Reine Angew. Math. 673 (2012), 1-31.
  • Lusztig's conjecture as a moment graph problem, preprint 2007, arXiv:0712.3909, Bull. London Math. Soc. 42(6) (2010), 957-972.
  • Sheaves on affine Schubert varieties, modular representations and Lusztig's conjecture, preprint 2007, arXiv:0711.0871, J. Amer. Math. Soc. 24 (2011), 133-181.
  • The multiplicity one case of Lusztig's conjecture, preprint 2006, math.RT/0607501, Duke Math. J. 153 (2010), 551-571.
  • Kazhdan-Lusztig theory via sheaves on Bruhat graphs, preprint 2005, math.RT/0512311 , in "Algebraic and Geometric Combinatorics" (Anogia, Crete, 2005), 195-204, Contemp. Math. 423 (2007).
  • The combinatorics of Coxeter categories, preprint 2005, math.RT/0512176 , Trans. Amer. Math. Soc. 360, no. 8, (2008), 4211-4233.
  • Sheaves on moment graphs and a localization of Verma flags, preprint 2005, math.RT/0505108, Adv. Math. 217 (2008), 683-712.
  • The combinatorics of category O for symmetrizable Kac-Moody algebras preprint 2003, math.RT/0305378, Transform. Groups 11 (2006), No. 1, 29-49.
  • Centers and translation functors for category O over symmetrizable Kac-Moody algebras, Math. Z. 243 (2003), No. 4, 689-717.
  • Zentren deformierter Darstellungskategorien und Verschiebungsfunktoren, Dissertation, Universität Freiburg (2001), pdf

Skripten

  • Lineare Algebra I:Wintersemester 2011/12: pdf
  • Lineare Algebra II: Sommersemester 2012: pdf
  • Algebra II: Ringe und Moduln im Wintersemester 2009/10: pdf
  • Moment graphs in representation theory and topology, Vortragsreihe in Köln, September/Oktober 2009: pdf (englisch)
  • Vorlesung zu Bruhatgraphen im Wintersemester 2008/09: pdf (englisch)
  • Darstellungstheorie von Lie-Algebren im Wintersemester 2012/13: pdf
  • Algebra im Wintersemester 2010: Gruppen, Ringe, Körper, Galois-Theorie und Transzendenz von Pi: pdf

Lecture Notes

Shanghai Lectures on Characters of representations and the topology of flag varieties

  • Lecture 1, Representations of algebraic groups: pdf
  • Lecture 2, Representations of modular Lie algebras: pdf
  • Lecture 3, Steinberg's tensor product theorem and Lusztig's conjecture: pdf
  • Lecture 4, Kazhdan-Lusztig theory: pdf
  • Lecture 5, The modular multiplicity conjecture and periodic polynomials: pdf
  • Lecture 6, Moment graphs: pdf
  • Lecture 7, Perverse sheaves and parity sheaves: pdf
  • Lecture 8, Proofs of multiplicity conjectures: pdf