Related papers: Gabor-type Frames from Generalized Weyl-Heisenberg…

We consider a class of relative $n$-Calabi--Yau dg-algebras, referred to as relative Ginzburg algebras, associated with marked surfaces equipped with a decomposition into $n$-gons ($n$-angulation). We relate their derived categories to the…

Let X be the group of weights of a maximal torus of a simply connected semisimple group over C and let W be the Weyl group. The semidirect product W(Q\otimes X/X) is called the extended Weyl group. There is a natural C(v)-algebra H called…

It is shown that the Baer-Kaplansky theorem can be extended to all abelian groups provided that the rings of endomorphisms of groups are replaced by trusses of endomorphisms of corresponding heaps. That is, every abelian group is determined…

We extend previous work on Hrushovski's stabilizer's theorem and prove a measure-theoretic version of a well-known result of Pillay-Scanlon-Wagner on products of three types. This generalizes results of Gowers on products of three sets and…

We examine the gauge generating nature of the translational subgroup of Wigner's little group for the case of massless tensor gauge theories and show that the gauge transformations generated by the translational group is only a subset of…

We consider for structure groups ${\rm SU}(n)\,\subset\, {\rm SL}(n,\mathbb C)$ a densely defined toric structure on the moduli of framed parabolic sheaves on a three-punctured sphere, which degenerates to an actual toric structure. In…

The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…

The generalized diamond group is the semi-direct product $G$ of the abelian group ${\mathbb R}^m$ by the $(2n+1)$-dimensional Heisenberg group $H_n$. We construct the generic representations of $G$ on the Fock space by extending those of…

We develop tools for determining the gauge theory resulting from a configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau 3-fold, in the presence of additional flavor D7-branes with general embeddings. Two main…

We construct \'etale generalized Heisenberg group covers of hyperelliptic curves over number fields. We use these to produce infinite families of quadratic extensions of cyclotomic fields that admit everywhere unramified generalized…

We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial…

We show that the general theory of relativity can be formulated in the language of Weyl geometry. We develop the concept of Weyl frames and point out that the new mathematical formalism may lead to different pictures of the same…

We describe a connection between two seemingly different problems: (a) the construction of projections in noncommutative tori, (b) the construction of tight Gabor frames. The present investigation relies an interpretation of projective…

We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$…

We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…

In this paper, \( L, M, N, R \) are positive integers, and \( \mathbb{S} \) is an \( N \)-periodic subset of \( \mathbb{Z} \). The space \( \ell^2(\mathbb{S}, \mathbb{C}^R) \) denotes the Hilbert space of vector-valued square-summable…

We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…

We prove that an overcomplete Gabor frame in $ \ell^2(\mathbf Z)$ by a finitely supported sequence is always linearly dependent. This is a particular case of a general result about linear dependence versus independence for Gabor systems in…

We extend the notion of generalized Whittaker models by allowing them to be built upon smooth irreducible representations of unipotent subgroups of a $p$-adic reductive group that are not necessarily characters, nor induced from Weil…

Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studied. Using such transformations, quantum linear evolution…