Related papers: Kostka systems and exotic t-structures for reflect…

We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite…

We develop the theory of equivariant, ultra Kolyvagin systems to bypass structural limitations of the Euler system machinery over infinite rings. By utilizing collections of classes living in the exterior powers of patched Selmer groups --…

In this paper the authors investigate infinite-dimensional representations $L$ in blocks of the relative (parabolic) category ${\mathcal O}_S$ for a complex simple Lie algebra, having the property that the cohomology of the nilradical with…

Recently we have used the Carlitz exponential map to define a finitely generated submodule of the Carlitz module having the right properties to be a function field analogue of the group of units in a number field. Similarly, we constructed…

We introduce the new concept of silting modules. These modules generalise tilting modules over an arbitrary ring, as well as support $\tau$-tilting modules over a finite dimensional algebra recently introduced by Adachi, Iyama and Reiten.…

We study the exotic t-structure on the derived category of coherent sheaves on two-block Springer fibre (i.e. for a nilpotent matrix of type (m+n,n) in type A). The exotic t-structure has been defined by Bezrukavnikov and Mirkovic for…

Let G be a connected reductive algebraic group over an algebraically closed field k, with simply connected derived subgroup. The exotic t-structure on the cotangent bundle of its flag variety T^*(G/B), originally introduced by…

A finite element cochain complex on Cartesian meshes of any dimension based on the H1-inner product is introduced. It yields H1-conforming finite element spaces with exterior derivatives in H1. We use a tensor product construction to obtain…

Double Kostka polynomials are polynomials indexed by a pair of double partitions. As in the ordinary case, double Kostka polynomials are defined in terms of Schur functions and Hall-Littlewood functions associated to double partitions. In…

We show that indecomposable exact module categories over the category Rep H of representations of a finite-dimensional Hopf algebra H are classified by left comodule algebras, H-simple from the right and with trivial coinvariants, up to…

The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line,…

We give a type-independent construction of an explicit basis for the semi-invariant harmonic differential forms of an arbitrary pseudo-reflection group in characteristic zero. Our "top-down" approach uses the methods of Cartan's exterior…

The Kochen-Specker theorem states that a 3-dimensional complex Euclidean space admits a finite configuration of projective lines such that the corresponding quantum observables (the orthogonal projectors) cannot be assigned with 0 and 1…

This paper is devoted to an exposition of the Koszul complex of a supermodule and its Berezinian from an intrinsic and as general as possible point of view. As an application, an analogue to Bott's formula in the supercommutative setting…

We show that the KZ system has a purely topological interpretation in the sense that it may be understood as a variation of complex mixed Hodge structure whose successive pure weight quotients are polarized. This in a sense completes and…

We introduce the concept of a strongly t-logarithmic t-generating set for a Z[t,t^{-1}]-module, which enables us to prove that a large class of soluble groups are not almost convex. We also prove some results about dead-end depth.

We report about results revolving around Kostka-Foulkes and parabolic Kostka polynomials and their connections with Representation Theory and Combinatorics. It appears that the set of all parabolic Kostka polynomials forms a semigroup,…

We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to…

The method of constrained Hamiltonian systems can be used to reduce Fock modules. It is applied to the Virasoro algebra, where a possibly new realization is found.

In this paper we prove that the cohomology groups with compact support of stacks of shtukas are modules of finite type over a Hecke algebra. As an application, we extend the construction of excursion operators, defined by V. Lafforgue on…