Institut de Mathématiques de Jussieu (IMJ)

Équipe des groupes finis

Nicolas Libedinsky

Research interests

I'm working on Soergel's category of bimodules. This is a categorification of the Hecke algebra of a Coxeter System. It is conceved in part to solve Kazhdan-Lusztig positivity conjecture, to solve Lusztig conjecture in algebraic groups and it's closely related to Khovanov homological invariants of links.

My PHD thesis (defended in November 2008) is available here and

my CV is available here.

Submitted papers

• New bases of some Hecke algebras via Soergel bimodules, preprint 2009 math.RT/arXiv:0907.0031v1 .
  

This is a first attempt to find explicitely Soergel indecomposable bimodules for extra-large Coxeter systems. I expect that a generalization of this methods will give a proof of Soergel's (and Kazhdan-Lusztig positivity) conjecture for large Coxeter systems.

Published Papers

• Presentation of right-angled Soergel categories by generators and relations, to appear in Journal of Pure and Applied Algebra , math.RT/arXiv:0810.2395v1 .
  

I find a presentation of Soergel category (as a tensor category) by generators and relations in the right-angled Coxeter group case.

• Équivalences entre conjectures de Soergel, Journal of Algebra 320 (2008) 2695-2705, math.RT/arXiv:0802.3031v1 .
  

I prove that in Soergel's conjecture it is equivalent to use the "easy" geometric representation or the "difficult" reflection faithful representation used before.

• Sur la catégorie des bimodules de Soergel, Journal of Algebra 320 (2008) 2675-2694, math.RT/arXiv:0707.3603v2.
  

I find explicitly all morphisms in Soergel's category and between projective objects in the principal block of BGG category O.

In preparation

• Positivity of asymptotic Kazhdan-Lusztig polynomials.

  In this paper I continue the work of my last paper "New basis..." and I reduce Soergel's conjecture in the extra-large case to a -in some sense- "local problem" that I beleive is much easier to solve. In particular I prove Soergel's conjecture for a large class of elements in the extra-large case.

Administration

• In charge, with Pierre-Guy Plamondon, of the seminar of PhD students of finite groups (from 2007).

Other activities

• Criticas euro mundo global
  

Some links

Raphaël Rouquier(My former advisor)
L'équipe des Groupes Finis
My family

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Institut Mathématique de Jussieu - Fondation Sciences Mathématiques de Paris - Fédération de recherche Mathématiques Paris Centre