Related papers: Generalised column removal for graded homomorphism…

The submodule structure of general Specht modules in prime characteristic is a difficult open problem. Kleshchev and Sheth [Journal of Algebra, 221(2), pp.705-722] gave a combinatorial description of the submodule structure of Specht…

Let G be a symplectic or orthogonal complex Lie group with Lie algebra g. As a G-module, the decomposition of the symmetric algebra S(g) into its irreducible components can be explicitely obtained by using identities due to Littlewood. We…

We formalize some known categorical equivalences to give a rigorous treatment of smooth representations of p-adic general linear groups, as ungraded modules over quiver Hecke algebras of type A. Graded variants of RSK-standard modules are…

Let $A$ be a differential graded algebra with cohomology ring $H^*A$. A graded module over $H^*A$ is called \emph{realisable} if it is (up to direct summands) of the form $H^*M$ for some differential graded $A$-module $M$. Benson, Krause…

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category…

In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators ($\mathcal{D}$-modules), and reformulate the…

This paper introduces (graded) skew cellular algebras, which generalise Graham and Lehrer's cellular algebras. We show that all of the main results from the theory of cellular algebras extend to skew cellular algebras and we develop a…

The elementary divisors of the Gram matrices of Specht modules S^lambda over the symmetric group are determined for two-row partitions and for two-column partitions lambda. More precisely, the subquotients of the Jantzen filtration are…

Let $E$ be the natural representation of the special linear group $\mathrm{SL}_2(K)$ over an arbitrary field $K$. We use the two dual constructions of the symmetric power when $K$ has prime characteristic to construct an explicit…

Let g be a complex reductive Lie algebra with Cartan algebra h. Hotta and Kashiwara defined a holonomic D-module M, on g x h, called Harish-Chandra module. We relate gr(M), an associated graded module with respect to a canonical Hodge…

The paper concerns Hochschild cohomology of a commutative algebra S, which is essentially of finite type over a commutative noetherian ring K and projective as a K-module, with coefficients in an S-module M. It is proved that vanishing of…

We study the representation theory of a generalized graded Hecke algebra associated to a complex reflection group of type G(r,1,n), defined by Ram and Shepler. We use a realization of this algebra in the corresponding symplectic reflection…

Let $\mathcal{A}$ be a quantized ($K$-theoretic) BFN Coulomb branch with $G=\mathbb{C}^*$ and any $N$, that is, $\mathcal{A}$ is a generalized Weyl or $q$-Weyl algebra. Let $M$ be an $\mathcal{A}$-$\overline{\mathcal{A}}$ bimodule. Choosing…

The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the…

We prove the vanishing of bounded cohomology with separable dual coefficients for many groups of interest in geometry, dynamics, and algebra. These include compactly supported structure-preserving diffeomorphism groups of certain manifolds;…

We introduce the notion of support equivalence for (co)module algebras (over Hopf algebras), which generalizes in a natural way (weak) equivalence of gradings. We show that for each equivalence class of (co)module algebra structures on a…

Consider a standard representation $\pi_{st}$ of a quasi-split reductive p-adic group G. The generalized injectivity conjecture, posed by Casselman and Shahidi, asserts that any generic irreducible subquotient $\pi$ of $\pi_{st}$ is…

We observe that on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of characteristic $p> h$ (where $h$ is the Coxeter number), with a given (generalized) central character are…

Using combinatorics of Young tableaux, we give an explicit construction of irreducible graded modules over Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients $R^{\lambda}$ of type $A_{n}$. Our construction is compatible…

We construct a class $\Theta_{\mathscr{R}}$ of homomorphisms from a Specht module $S_{\mathbb{Z}}^{\lambda}$ to a signed permutation module $M_{\mathbb{Z}}(\alpha|\beta)$ which generalises James's construction of homomorphisms whose…