Séminaire d'Algèbre

salle 001, rez de chaussée, 11 rue Pierre et Marie Curie - 75005 Paris

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Lundi 12 mars 2018 à 14h00

Julian KULSHAMMER (Stuttgart), Existence and uniqueness of exact Borel subalgebras.
[Quasi-hereditary algebras and their infinite analogues, highest weight categories, appear frequently in many areas of representation theory. In joint work with S. Koenig and S. Ovsienko, we showed that every quasi-hereditary algebra can up to Morita equivalence be obtained as the dual of a coring object in the tensor category of bimodules over a directed algebra, the exact Borel subalgebra.
Under an additional assumption, the exact Borel subalgebra as well as the coring object are in fact unique up to isomorphism. This is joint work with V. Miemietz.]

Lundi 26 mars 2018 à 14h00

Lara BOSSINGER (Cologne), Toric degenerations from representation theory, tropical geometry and cluster algebras.
[In this talk I will explain how toric degenerations arise from the tropicalization of a (projective) variety. In the context of varieties that are interesting from a representation theoretic point of view (e.g. Grassmannians or flag varieties) I will explain a construction of toric degenerations due to Fang, Fourier, and Littelmann called birational sequences and compare to degenerations obtained from the cluster structure on these varieties. I will present many examples and some results on how these constructions are related.
For example, I will present computational results on the tropicalization of the full flag variety for n=4 and 5 and compare the obtained toric degenerations to some classical degenerations from representation theory (string polytopes and the FFLV polytope) that arise in the context of birational sequences.]

Lundi 9 avril 2018 à 14h00

Yann PALU (Amiens)

Lundi 16 avril 2018 à 14h00

Alexey SEVASTYANOV (Aberdeen), Zhelobenko operators, Schubert cells and q-W algebras.
[In the beginning of the 80th Zhelobenko suggested a formula for a projection operator onto the subspace of singular vectors for modules from the BGG category O for a complex semisimple Lie algebra. This projection operator and some its modifications called Zhelobenko operators are related to the problem of finding an explicit description for the space of invariant regular functions with respect to the conjugation action of the unipotent radical of a semisimple algebraic group on the Borel subalgebra. In this talk I shall discuss a similar construction in case of the so-called q-W algebras which are related to the category of generalized Gelfand-Graev representations for quantum groups. The underlying geometry in this case is the geometry of the conjugation action of certain unipotent groups on Schubert cells. Using Zhelobenko operators I shall suggest an explicit description for generators of Poisson q-W algebras. Surprisingly, the results that will be presented in this talk have no direct analogues for complex semisimple Lie algebras and for ordinary W-algebras associated to them.]

Lundi 30 avril 2018 à 14h00

Michel van den BERGH (Hasselt)

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Groupes, représentations et géométrie.
Dernière modification : le 21/03/2018