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Building on a geometric counterpart of Steinberg's tensor product formula for simple representations of a connected reductive algebraic group $G$ over a field of positive characteristic, and following an idea of…

In this paper, we give a more down-to-earth introduction to the connection between Gelfand-Tsetlin modules over $\mathfrak{gl}_n$ and diagrammatic KLRW algebras, and develop some of its consequences. In addition to a new proof of this…

We show that the Koszul functor of a homologically smooth graded gentle algebra can be realized as the half rotation in a geometric model. As a byproduct, we prove an intersection-dim formula involving the Koszul functor.

In this survey, we present a detailed guide on using the computer algebra system OSCAR to compute monomial bases for simple, finite-dimensional modules of simple, complex Lie algebras. We will also demonstrate how to determine monomial…

We prove a short, root-system uniform, combinatorial classification of Levi-spherical Schubert varieties for any generalized flag variety $G/B$ of finite Lie type. We apply this to the study of multiplicity-free decompositions of a Demazure…

In Part 1, we classify (indecomposable) objects in the perfect derived category $\mathrm{per}\Lambda$ of a graded skew-gentle algebra $\Lambda$, generalizing technique/results of Burban-Drozd and Deng to the graded setting. We also use the…

The pair of real reductive groups $(G,H)=(\operatorname{GL}(n+1,\mathbb{R}),\operatorname{GL}(n,\mathbb{R}))$ is a strong Gelfand pair, i.e. the multiplicities $\dim\operatorname{Hom}_H(\pi|_H,\tau)$ are either $0$ or $1$ for all…

For Brauer graph algebras, tilting mutation is compatible with flip of Brauer graphs. The aim of this paper is to generalize this result to the class of Brauer configuration algebras introduced by Green and Schroll recently. More precisely,…

Let $G_\mathbb R$ be a connected real reductive group and let $X$ be the corresponding complex symmetric variety under the Cartan bijection. We construct a canonical equivalence between the relative Satake category of $G(\mathcal…

The notion of defect of a finitely presented functor on a module category is extended to arbitrary additive functors. The new defect and the contravariant Yoneda embedding form a right adjoint pair. The main result identifies the defect of…

We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.

For $G = \mathrm{GL}_n$ or $\mathrm{U}_n$ defined over a finite field of characteristic $p$, we refine a result of Bonnaf\'e and Kessar on the saturatedness of the Curtis homomorphism $\mathrm{Cur}^G$ by describing the image of…

Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the derived category D(Mod R). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with…

We introduce the notion of ``finite general representation type'' for a finite-dimensional algebra, a property related to the ``dense orbit property'' introduced by Chindris-Kinser-Weyman. We use an interplay of geometric, combinatorial,…

Let $G=PGL(2,Q_q)$. In this paper we shall investigate the group of measurable currents taking values in $G$. The key observation is that $G$ is acting by automorphisms on a homogeneous tree, which will play the role of the upper half plane…

In this article, we prove that if $(\mathcal A ,\mathcal B,\mathcal C)$ is a recollement of extriangulated categories, then $n$-cotorsion pairs in $\mathcal A$ and $\mathcal C$ can induce $n$-cotorsion pairs in $\mathcal B$. Conversely,…

In this paper, we introduce a family of functors denoted $\mathscr{F}_b$ that act on algebraic D-modules and generate modules over N=2 superconformal algebras. We prove these functors preserve irreducibility for all values of $b$, with a…

Let $B \subseteq A$ be an extension of finite dimensional algebras. We provide a sufficient condition for the existence of triangle equivalences of singularity categories (resp. Gorenstein defect categories) between $A$ and $B$. This result…

In this paper, we introduce a new family of functors from the category of modules for the Weyl algebra to the category of modules for the super-Virasoro algebras. The properties of these functors are investigated, with an emphasis on…

We develop an algebraic approach to the branching of representations of the general linear Lie superalgebra $\mathfrak{gl}_{p|q}({\mathbb C})$, by constructing certain super commutative algebras whose structure encodes the branching rules.…