Related papers: Quadrature Mirror Filters and Loop Groups
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…
In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup \Gamma^0(N), with respect to the usual fundamental domain FN, where N is assumed prime. The cycles Q_1, . . ., Q_n that…
Let $\mathfrak{g}$ be a complex simple Lie algebra and $U_q(\hat{\mathfrak{g}})$ the corresponding quantum affine algebra. We prove that every irreducible finite-dimensional $U_q(\hat{\mathfrak{g}})$-module gives rise to a family of…
When the standard representation of a crystallographic Coxeter group is reduced modulo an odd prime p, one obtains a finite group G^p acting on some orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p will often…
Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories that can be made all-loop finite, leading to a severe reduction of the free parameters. We review the investigation of FUTs based on SU(5) in the context of…
In this paper, we settle a long-standing problem on the connectivity of spaces of finite unit norm tight frames (FUNTFs), essentially affirming a conjecture first appearing in [Dykema and Strawn, 2003]. Our central technique involves…
We define some rings of power series in several variables, that are attached to a Lubin-Tate formal module. We then give some examples of (\phi,\Gamma)-modules over those rings. They are the global sections of some reflexive sheaves on the…
Let $\text{U}(n,\mathbb{F}_{q^2})$ denote the subgroup of unitary matrices of the general linear group $\text{GL}(n,\mathbb{F}_{q^2})$ which fixes a Hermitian form and $M\geq 2$ an integer. This is a companion paper to the previous works…
Starting from mirror pairs consisting only of linear (framed A-type) quivers, we demonstrate that a wide class of three-dimensional quiver gauge theories with N=4 supersymmetry and their mirror duals can be obtained by suitably gauging…
We give a criterion for a finitely generated odd-angled Coxeter group to have a proper finite index subgroup generated by reflections. The answer is given in terms of the least prime divisors of the exponents of the Coxeter relations.
We propose a purely group-theoretical method for describing the S-matrix in quantum field theory with dynamical symmetry. In this approach, the Heisenberg S-matrix in a QFT with dynamical symmetry is an intertwining operator between unitary…
A hyperfinite $II_1$ subfactor may be obtained from a symmetric commuting square via iteration of the basic construction. For certain commuting squares constructed from Hadamard matrices, we describe this subfactor as a group-type inclusion…
We investigate the convex hulls of the eight dihedral symmetry classes of $n \times n$ alternating sign matrices, i.e., ASMs invariant under a subgroup of the symmetry group of the square. Extending the prefix-sum description of the ASM…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
We study polynomial functors of degree 2, called quadratic, with values in the category of abelian groups $Ab$, and whose source category is an arbitrary category $\C$ with null object such that all objects are colimits of copies of a…
Quantum signal processing (QSP) is a framework for implementing certain polynomial functions via quantum circuits. To construct a QSP circuit, one needs (i) a target polynomial $P(z)$, which must satisfy $\lvert P(z)\rvert\leq 1$ on the…
Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of…
This paper determines the relationship between the geometry of retractions and the combinatorics of folded galleries for arbitrary affine buildings, and so provides a unified framework to study orbits in affine flag varieties. We introduce…
We find a new geometric incarnation for the principal block in the category of modules over a quantum group at a root of unity, realizing it as a full subcategory of microsheaves on a certain affine Springer fiber. We also prove a related…
The possibility that gauge theories with chiral symmetry breaking below the conformal window exhibit an infrared fixed point is explored. With this assumption three aspects of pion physics are reproduced if the the quark mass anomalous…