Related papers: The Duflo-Serganova functor, vingt ans apr\`es

We study Duflo-Serganova functor for non-twisted affine Lie superalgebras and affine vertex superalgebras.

We study the Duflo-Serganova functor $\operatorname{DS}_x$ for the queer Lie superalgebra $\mathfrak{q}_n$ and for all odd $x$ with $[x,x]$ semisimple. For the case when the rank of $x$ is $1$ we give a formula for multiplicities in terms…

We discuss several points regarding symmetries of the Duflo-Serganova functor. In particular we give new constructions of Lie superalgebras, Lie supergroups, and associative superalgebras which act on the Duflo-Serganova functor. We connect…

We prove that the Duflo-Serganova functor $DS_x$ attached to an odd nilpotent element $x$ of $\mathfrak{osp}(m|2n)$ is semisimple, i.e. sends a semisimple representation $M$ of $\mathfrak{osp}(m|2n)$ to a semisimple representation of…

In this paper, we study the representations of the periplectic Lie superalgebra using the Duflo-Serganova functor. Given a simple $\mathfrak{p}(n)$-module $L$ and a certain element $x\in \mathfrak{p}(n)$ of rank $1$, we give an explicit…

Duflo--Serganova functors play an important role in the representation theory of Lie superalgebras. While it is desirable to understand the images of modules under DS, little is known beyond finite-dimensional representations. For general…

The Dulfo-Serganova functors DS are tensor functors relating representations of different Lie superalgebras. In this paper we study the behaviour of various invariants, such as the defect, the dual Coxeter number, the atypicality and the…

We consider several examples when the extension graph admits a bipartition compatible with the action of Duflo--Serganova functors.

We establish an explicit formula for the character of an irreducible finite-dimensional representation of $\mathfrak{gl}(m|n)$. The formula is a finite sum with integer coefficients in terms of a basis $\mathcal{E}_{\mu}$ (Euler characters)…

In this paper we study extensions between finite-dimensional simple modules over classical Lie superalgebras $\mathfrak{gl}(m|n), \mathfrak{osp}(M|2n)$ and $\mathfrak{q}_m$. We consider a simplified version of the extension graph which is…

These notes give an exposition of Deligne's theorem on the existense of super fiber functor.

This is a semi-expository article concerning Langlands functoriality and Deligne's conjecture on the special values of $L$-functions. The emphasis is on symmetric power $L$-functions associated to a holomorphic cusp form, while appealing to…

Let G be a connected complex reductive group and let K be a symmetric subgroup of G. We prove a formula for the Drinfeld-Gaitsgory functor for the dg-category of K-equivariant sheaves on the flag manifold of G in terms of the Matsuki…

This is the continuation of the study of differential graded (dg) vertex algebras previously defined by the authors. The goal of this paper is to construct a functor from the category of dg vertex Lie algebras to the category of dg vertex…

For the exceptional finite-dimensional modular Lie superalgebras $\mathfrak{g}(A)$ with indecomposable Cartan matrix $A$, and their simple subquotients, we computed non-isomorphic Lie superalgebras constituting the homologies of the odd…

Using adjoint representation we firstly classify two and three dimensional Lie super-bialgebras obtain from decomposable Lie superalgebras. In this way we complete the classification obtained by Eghbali et al., [J. Math. Phys. 51, 073503…

In 1971 Griffiths used a generating function to define polynomials in d variables orthogonal with respect to the multinomial distribution. The polynomials possess a duality between the discrete variables and the degree indices. In 2004…

We explain a direct topological proof for the multiplicativity of Duflo isomorphism for arbitrary finite dimensional Lie algebras, and derive the explicit formula for the Duflo map. The proof follows a series of implications, starting with…

The author (Bull. Math. Anal. App. 6(4)(2014):1-15), introduced a new fractional derivative, \[{}^\rho \mathcal{D}_a^\alpha f (x) = \frac{\rho^{\alpha-n+1}}{\Gamma({n-\alpha})} \, \bigg(x^{1-\rho} \,\frac{d}{dx}\bigg)^n \int^x_a…

We describe explicitly Lie superalgebra isomorphisms between the Lie superalgebras of first-order superdifferential operators on supermanifolds, showing in particular that any such isomorphism induces a diffeomorphism of the supermanifolds.…