Inna Entova Aizenbud
"Monoidal abelian envelopes and a conjecture of Benson-Etingof"
I will define what is an abelian envelope of a fixed rigid symmetric monoidal category, in the sense of Deligne. And give several examples and applications, both in characteristic zero and in positive characteristic.
Yasmine Fittouhi
"Weierstrass section for parapolic adjoint action in type A "
The first part on this talk, we revisit theorem's Richardson by using the notion of Weierstrass section. The second part, we will exhibit our construction of Weierstrass sections for the adjoint action of the derived algebra of a parabolic subalgebra $\mathfrak{p}'$ on its nilradical $\mathfrak{m}$ in type A, we will use the standard Young tableau build up with links (which turn to be a quiver ), in order to obtain the component of Weierstrass section; this construction has some a delicate points that would be explain. This combinatorial constriction will shed the light on key aspects that will lead us to interesting results.
Maria Gorelik
"Gruson-Serganova character formula and Duflo-Serganova functor"
The Dulfo-Serganova functor is a cohomology functor relating representation theory of Lie superalgebras of different ranks. This is a tensor functor preserving superdimension. Serganova conjectured that the image of a finite-dimensional simple module is semisimple. This conjecture for gl-type was established by Heidersdorf and Weissauer. I will sketch a proof of this result for osp-type. A key ingredient is the fact that we can define a parity for each finite-dimensional simple module in such a way that the Serre subcategory generated by even modules is semisimple and that the Dulfo-Serganova functor preserves these subcategories. Using the same parity we show that the supercharacter ring admits a basis consisting of Kac-Wakimoto type elements with the following property: the coefficients of the supercharacter of each simple module written in this basis have the same sign. This is a joint project with Thorsten Heidersdorf.
Lenny Makar-Limanov
"Centralizers of rank one in the first Weyl algebra have genus zero"
Take a in A_1 (the first Weyl algebra). Rank of the centralizer C(a) is the greatest common divisor of the orders of elements in C(a) (orders as differential operators). This note contains a proof of the following. Theorem. If the centralizer C(a) of a in A_1 (defined over the field of complex numbers) has rank 1 then C(a) can be embedded into a polynomial ring in one variable.
Thane Nampaisarn
"Parabolic Version of Extended Categories O for Root-Reductive Lie Algebras"
Abstract