Related papers: Gabor Frames for Quasicrystals, $K$-theory, and Tw…

This paper explores the representation of quantum computing in terms of unitary reflections (unitary transformations that leave invariant a hyperplane of a vector space). The symmetries of qubit systems are found to be supported by…

We consider the quantum affine vertex algebra $\mathcal{V}_{c}(\mathfrak{gl}_N)$ associated with the rational $R$-matrix, as defined by Etingof and Kazhdan. We introduce certain subalgebras $\textrm{A}_c (\mathfrak{gl}_N)$ of the completed…

We construct a new class of finite-dimensional C^*-quantum groupoids at roots of unity q=e^{i\pi/\ell}, with limit the discrete dual of the classical SU(N) for large orders. The representation category of our groupoid turns out to be tensor…

We study the hemisphere partition function of a three-dimensional $\mathcal{N}=4$ supersymmetric $U(N)$ gauge theory with one adjoint and one fundamental hypermultiplet -- the ADHM quiver theory. In particular, we propose a distinguished…

In the first part of the paper we describe the dual \ell^2(A)^{\prime} of the standard Hilbert C*-module \ell^2(A) over an arbitrary (not necessarily unital) C*-algebra A. When A is a von Neumann algebra, this enables us to construct…

The diffraction pattern of a quasicrystal admits as symmetry group a finite group G, and there exists a G-cluster C (a union of orbits of G) such that the quasicrystal can be regarded as a quasiperiodic packing of copies of C, generally,…

We realize the fundamental representations of quantum algebras via the supersymmetric Higgs mechanism in gauge theories with 8 supercharges on an $\Omega$-background. We test our proposal for quantum affine algebras, by probing the Higgs…

Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $\Gamma <G$ and $\Lambda < G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $\Gamma$ into…

We give a rigorous account and prove continuity properties for the correspondence between almost flat bundles on a triangularizable compact connected space and the quasi-representations of its fundamental group. For a discrete countable…

We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on…

Inspired by the work of Paterson on $C^{\ast}$-algebras of directed graphs, we show how to associate a groupoid $\mathfrak{G}_{\mathcal{G}}$ to an ultragraph $\mathcal{G}$ in such a way that the $C^*$-algebra of $\mathfrak{G}_{\mathcal{G}}$…

Ginzburg, Kapranov and Vasserot conjectured the existence of equivariant elliptic cohomology theories. In this paper, to give a description of equivariant spectra of the theories, we study an intermediate theory, quasi-elliptic cohomology.…

We introduce and study a new class of topological $G$-spaces generalizing the classical flag manifolds $G/T$ of compact connected Lie groups. These spaces, which we call the $m$-quasi-flag manifolds $ F_m = F_m(G,T) $, are topological…

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…

Let $(G,{\mathfrak I},N,S)$ be an affine topological Tits system, and let $\Gamma$ be a torsion free cocompact lattice in $G$. This article studies the coinvariants $H_0(\Gamma; C(\Omega,{\mathbb Z}))$, where $\Omega$ is the Furstenberg…

We present a time-frequency framework adapted to dispersive phase functions via a subdyadic geometry in phase space. On top of this geometry we construct stable Gabor frames with quantitative control of overlap, almost orthogonality, and…

Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B ${\bf 90}$, 165114 (2014)] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant $K$-theory, we…

We consider the problem in determining the countable sets $\Lambda$ in the time-frequency plane such that the Gabor system generated by the time-frequency shifts of the window $\chi_{[0,1]^d}$ associated with $\Lambda$ forms a Gabor…

The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, ${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic…

We establish the correspondence between, on one side, the possible gaugings and massive deformations of half-maximal supergravity coupled to vector multiplets and, on the other side, certain generators of the associated very extended…