Related papers: A note on control theorems for quaternionic Hida f…

We introduce a method for associating a chain complex to a module over a combinatorial category, such that if the complex is exact then the module has a rational Hilbert series. We prove homology--vanishing theorems for these complexes for…

The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…

We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal…

A quasi-hereditary algebra is an algebra equipped with a certain partial order $\unlhd$ on its simple modules. Such a partial order -- called a quasi-hereditary structure -- gives rise to a characteristic tilting module $T_{\unlhd}$ by a…

I employ methods from derived algebraic geometry to give a uniform moduli-theoretic construction of special cycle classes on integral models many Shimura varieties of Hodge type, including unitary, quaternionic, and orthogonal Shimura…

In this paper we describe an inductive machinery to investigate asymptotic behaviors of homology groups and related invariants of representations of certain graded combinatorial categories over a commutative Noetherian ring $k$, via…

We have studied irreducible real (respectively, quaternionic) Lie algebroid connections and prove that the Gauge theoretic moduli space has Hausdorff Hilbert manifold structure. This work generalises some known results about simple…

We revisit the characterisation of modules over non-unital $C^*$-algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier module characterises a class of modules which closely mirror the…

Let $k$ be a field of characteristic $0$, let $\mathsf{C}$ be a finite split category, let $\alpha$ be a 2-cocycle of $\mathsf{C}$ with values in the multiplicative group of $k$, and consider the resulting twisted category algebra…

We study the invariant subspaces of abelian operator algebras of finite split strict multiplicity. We give sufficient conditions for the reflexivity and hereditary reflexivity of these algebras.

In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] there is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. Such model can…

The notion of a Bing cell is introduced, and it is used to define invariants, link groups, of 4-manifolds. Bing cells combine some features of both surfaces and 4-dimensional handlebodies, and the link group \lambda(M) measures certain…

We show that the modular branching rule (in the sense of Harish-Chandra) on unipotent modules for finite unitary groups is piecewise described by particular connected components of the crystal graph of well-chosen Fock spaces, under…

We investigate various homotopy invariant formulations of commutative algebra in the context of rational homotopy theory. The main subject is the complete intersection condition, where we show that a growth condition implies a structure…

It was conjectured at the end of the book "Representation theory of Artin algebras" by M. Auslander, I. Reiten and S. Smalo that an Artin algebra with the property that its finitely generated indecomposable modules are up to isomorphism…

We consider bilinear pseudo-differential operators whose symbols posses Gevrey type regularity and may have a sub-exponential growth at infinity, together with all their derivatives. It is proved that those symbol classes can be described…

The algebraic notion of a pivotal module category was developed by Schaumann and Shimizu and is central to the description of boundary conditions in conformal field theory according to a proposal by Fuchs and Schweigert. In this paper, we…

Support $\tau$-tilting modules correspond to some classes of categorical objects bijectively, such as two-term tilting complexes for any finite dimensional symmetric algebra. This fact motivates us to classify support $\tau$-tilting modules…

Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which have right inverses but no left inverses…

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be…