Related papers: Notes on Restricted Inverse Limits of Categories

We compare derived categories of the category of strict polynomial functors over a finite field and the category of ordinary endofunctors on the category of vector spaces. We introduce two intermediate categories: the category of…

Higher categorical structures are often defined by induction on dimension, which a priori produces only finite-dimensional structures. In this paper we show how to extend such definitions to infinite dimensions using the theory of terminal…

We construct the polynomial induction functor, which is the right adjoint to the restriction functor from the category of polynomial representations of a general linear group to the category of representations of its Weyl group. This…

Let $G$ be the quantum $GL_n$ over a field of characteristic $p\neq 0$. In this paper we define the ring of twisted tilting modules of $G$. We give generators and relations for the ring of twisted tilting modules of quantum $GL_2(k)$. We…

Let $\phi:G\rightarrow G$ be an endomorphism of a finitely generated residually finite group. R.~Hirshon asked if there exists~$n$ such that the restriction of $\phi$ to $\phi^n(G)$ is injective. We give an example to show that this is not…

In this paper we study the subcategory of finite-length objects of the category of positive level integrable representations of a toroidal Lie algebra. The main goal is to characterize the blocks of the category. In the cases when the…

Let G be a finite group of order n and V an irreducible representation over the complex numbers of dimension d. For some nonnegative number e, we have n=d(d+e). If e is small, then the character of V has unusually large degree. We fix e and…

Let $G$ be a finite group and $P$ a Sylow $2$-subgroup of $G$. We obtain both asymptotic and explicit bounds for the number of odd-degree irreducible complex representations of $G$ in terms of the size of the abelianization of $P$. To do…

In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…

We study exact module categories over the representation categories of finite-dimensional quasi-Hopf algebras. As a consequence we classify exact module categories over some families of pointed tensor categories with cyclic group of…

We propose a definition of higher inductive types in $(\infty,1)$-categories with finite limits. We show that the $(\infty,1)$-category of $(\infty,1)$-categories with higher inductive types is finitarily presentable. In particular, the…

In this paper we prove a local converse theorem for GL_n over the archimedean local fields, which characterizes an infinitesimal equivalence class of irreducible admissible representations of GL_n(R) (or GL_n(C)) in terms of twisted…

We work with $FI$-modules over a small preadditive category $\mathcal R$, viewed as a ring with several objects. Our aim is to study torsion theories for $FI$-modules. We are especially interested in torsion theories on finitely generated…

The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…

Degree bounds for algebra generators of invariant rings are a topic of longstanding interest in invariant theory. We study the analogous question for field generators for the field of rational invariants of a representation of a finite…

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

In this paper, we prove certain multiplicity one theorems and define twisted gamma factors for irreducible generic cuspidal representations of split $G_2$ over finite fields $k$ of odd characteristic. Then we prove the first converse…

A generalization of the definition of a one-dimensional improper integral with a finite limit is presented. The new definition extends the range of valid integrals to include integrals which were previously considered to not be integrable.…

In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to…