Related papers: Products of stabilizing representations
We introduce a technique for proving quantitative representation stability theorems for sequences of representations of certain finite linear groups over a field of characteristic zero. In particular, we prove a vanishing result for higher…
We define a new class of racks, called finitely stable racks, which, to some extent, share various flavors with Abelian groups. Characterization of finitely stable Alexander quandles is established. Further, we study twisted rack dynamical…
In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
We study special systems with infinitely many degrees of freedom with regard to dynamical evolution and fulfillment of constraint conditions. Attention is focused on establishing a meaningful functional framework, and for that purpose,…
A star-product formalism describing deformations of the standard quantum mechanical harmonic oscillator is introduced. A number of existing generalized oscillators occur as particular choises of star-products between the elements of the…
We study the convergence of a sequence of finite Blaschke products of a fix order toward a rotation. This would enable us to get a better picture of a characterization theorem for finite Blaschke products.
We give a new technique for constructing presentations by generators and relations for representations of groups like $SL_n(\mathbb{Z})$ and $Sp_{2g}(\mathbb{Z})$. Our results play an important role in recent work of the authors calculating…
Recently, it has been shown constructively how a finite set of hypergeometric products, multibasic hypergeometric products or their mixed versions can be modeled properly in the setting of formal difference rings. Here special emphasis is…
We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include…
The "back-stabilization number" for products of Schubert polynomials is the distance the corresponding permutations must be shifted before the structure constants stabilize. We give an explicit formula for this number and thereby prove a…
Using factorization homology with coefficients in twisted commutative algebras (TCAs), we prove two flavors of higher representation stability for the cohomology of (generalized) configuration spaces of a scheme/topological space $X$.…
We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…
From a root system, one may consider the arrangement of reflecting hyperplanes, as well as its toric and elliptic analogues. The corresponding Weyl group acts on the complement of the arrangement and hence on its cohomology. We consider a…
In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups $\mathcal{U}$. We encode this large amount of data into a convenient abelian category $\mathcal{A}\mathcal{U}$…
An operation of a coproduct of representations of a bialgebra is defined. The coproduct operation for representations of the Hopf algebra of functions on the quantum group $SU_{q}(2)$ is investigated. A notion of a stable representation…
In this paper we develop machinery for studying sequences of representations of any of the three families of classical Weyl groups, extending work of Church, Ellenberg, Farb, and Nagpal on the symmetric groups S_n to the signed permutation…
In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…
We investigate the representation theory of the crossed-product C*-algebra associated to a compact group G acting on a locally compact space X when the stability subgroups vary discontinuously. Our main result applies when G has a principal…
In this article we study algebraic stability for rational skew products in two dimensions $\phi : X \dashrightarrow X$, i.e. maps of the form $\phi(x, y) = (\phi_1(x), \phi_2(x, y))$. We prove that when $X$ is a birationally ruled surface…