Related papers: Semicanonical bases and preprojective algebras

We study preprojective algebras associated to either finite dimensional hereditary algebras, or locally finite hereditary tensor algebras, and in particular show that they have global dimension two in non-Dynkin type. Moreover, starting…

We define a binary operation on the set of irreducible components of Lusztig's nilpotent varieties of a quiver. We study commutativity, cancellativity and associativity of this operation. We focus on rigid irreducible components and discuss…

The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split…

Let $X$ be a compact connected Riemann surface of genus $g \geq 2$ and $G$ a connected reductive affine algebraic group over $\mathbb{C}$. We prove the semiprojectivity of the moduli spaces of semistable $G$-Higgs bundles and $G$-bundles…

For an irreducible affine variety $X$ over an algebraically closed field of characteristic zero we define two new classes of modules over the Lie algebra of vector fields on $X$ - gauge modules and Rudakov modules, which admit a compatible…

We study Demazure modules which occur in a level $\ell$ irreducible integrable representation of an affine Lie algebra. We also assume that they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie…

Let $\Lambda$ be a $\mathbb{Z}$-graded artin algebra. Two classical results of Gordon and Green state that if $\Lambda$ has only finitely many indecomposable gradable modules, up to isomorphism, then $\Lambda$ has finite representation…

We construct a universal continuous invariant bilinear form for the Lie algebra of compactly supported sections of a Lie algebra bundle in a topological sense. Moreover we construct a universal continuous central extension of a current…

Let G be a semisimple algebraic group over an algebraically closed field of characteristic p>0, and let g be its Lie algebra. The crucial Lie algebra representations to understand are those associated with the reduced enveloping algebra…

We establish a canonical basis character formula for the irreducible modules in arbitrary parabolic BGG-type categories, including the category of finite-dimensional modules, for finite $W$-superalgebras of type $A$. These categories…

We define the degenerate two boundary affine Hecke-Clifford algebra $\mathcal{H}_d$, and show it admits a well-defined $\mathfrak{q}(n)$-linear action on the tensor space $M\otimes N\otimes V^{\otimes d}$, where $V$ is the natural module…

We show that the quantum Frobenius morphism constructed by Lusztig in the setting of the quantum enveloping algebra specialized at a root of unity admits a multiplicative splitting (non unital). We also find a basis of the toral part of the…

We construct a bijection between admissible representations for an affine Lie algebra $\mathfrak{g}$ at boundary admissible levels and $\mathbb{C}^\times$ fixed points in homogeneous elliptic affine Springer fibres for the Langlands dual…

We prove irreducible components of moduli spaces of semistable representations of skewed-gentle algebras, and more generally, clannish algebras, are isomorphic to products of projective spaces. This is achieved by showing irreducible…

The graded cellularity of Libedinsky Double Leaves, which form a basis for the endomorphism ring of the Bott_Samelson_Soergel bimodules, allows us to view the Kazhdan_Lusztig polynomials as graded decomposition numbers. Using this point of…

One proves that each almost local-global semihereditary ring has the stacked basis property and is almost Bezout. If M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annhilators is…

Let $G$ be a compact Lie group. We introduce a semiclassical framework, called Borel-Weil calculus, to investigate $G$-equivariant (pseudo)differential operators acting on $G$-principal bundles over closed manifolds. In this calculus, the…

We study the finite dimensional modules on the half-quantum group u_q^+ at a root of unity q, whose action can be extended to u_q (quotient of the quantized enveloping algebra of sl_2). We derive decomposition formulas of the tensor product…

In this article we investigate the interplay between stem covers, the Schur multiplier of Leibniz crossed modules and the non-abelian exterior product of Leibniz algebras. In concrete, we obtain a six-term exact sequence associated to a…

We study certain family of finite-dimensional modules over the Yangian $Y(gl_N)$. The algebra $Y(gl_N)$ comes equipped with a distinguished maximal commutative subalgebra $A(gl_n)$ generated by the centres of all algebras in the chain…