相关论文: Reproducing formulas for generalized translation i…

We study a class of duality transformations in generalised Z(2) gauge theories and Ising models on two- and three-dimensional compact lattices. The theories are interpreted algebraically in terms of the structure constants of a…

For a finite group $G$, the notion of a $G$-transfer system provides homotopy theorists with a combinatorial way to study equivariant objects. In this paper, we focus on the properties of transfer systems for non-abelian groups. We…

For a group $G$ first order definable in a structure $M$, we continue the study of the "definable topological dynamics" of $G$. The special case when all subsets of $G$ are definable in the given structure $M$ is simply the usual…

This paper extends and applies algebraic invariants and constructions for mixing finite group extensions of shifts of finite type. For a finite abelian group G, Parry showed how to define a G-extension S_A from a square matrix A over Z_+G,…

We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map.…

Let k be an algebraically closed field of characteristic p>0. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the general linear group over k in terms of cap diagrams under…

We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian.…

We consider compact locally symmetric spaces $\Gamma\backslash G/H$ where $G/H$ is a non-compact semisimple symmetric space and $\Gamma$ is a discrete subgroup of $G$. We discuss some features of the joint spectrum of the (commutative)…

We use geometric invariant theory (GIT) to construct a large class of compactifications of the moduli space M_{0,n}. These compactifications include many previously known examples, as well as many new ones. As a consequence of our GIT…

Gabardo and Nashed have studied nonuniform wavelets based on the theory of spectral pairs for which the associated translation set $\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but a spectrum…

Let $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ be the class of normalized analytic functions $f$ defined in the region $|z|<1$ and satisfying \begin{align*} {\rm Re\,}…

We generalize the classical semi-continuity theorem for GIT (semi)stable loci under variations of linearizations to a relative situation of an equivariant projective morphism from X to an affine base S. As an application to moduli problems,…

This paper proposes a novel approach to domain translation. Leveraging established parallels between generative models and dynamical systems, we propose a reformulation of the Cycle-GAN architecture. By embedding our model with a…

Let L:= Z^D be the D-dimensional lattice and let A^L be the Cantor space of L-indexed configurations in some finite alphabet A, with the natural L-action by shifts. A `cellular automaton' is a continuous, shift-commuting self-map F of A^L,…

We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…

We study closed subspaces of $L^2(X)$, where $(X, \mu)$ is a $\sigma$-finite measure space, that are invariant under the unitary representation associated to a measurable action of a discrete countable LCA group $\Gamma$ on $X$. We provide…

We show the full structure of the frame set for the Gabor system $\mathcal{G}(g;\alpha,\beta):=\{e^{-2\pi i m\beta\cdot}g(\cdot-n\alpha):m,n\in\Bbb Z\}$ with the window being the Haar function $g=-\chi_{[-1/2,0)}+\chi_{[0,1/2)}$. The…

Let $W$ be a finite-dimensional representation of a reductive algebraic group $G$. The invariant Hilbert scheme $\mathcal{H}$ is a moduli space that classifies the $G$-stable closed subschemes $Z$ of $W$ such that the affine algebra $k[Z]$…

Bi-incomplete Tambara functors over a group $G$ can be understood in terms of compatible pairs of $G$-transfer systems. In the case of $G = C_{p^n}$ , Hill, Meng and Li gave a necessary and sufficient condition for compatibility and…

It is known that, in general, an affine or Gabor AP-frame is an $L^2(\mathbb{R})$-frame and conversely. In part as a consequence of the Ergodic Theorem, we prove a necessary and sufficient condition for an affine (wavelet) system…