Related papers: Abstract Harmonic Analysis on the General Linear G…
We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible…
In this paper, an explicit expression for the Casimir operator (or the Casimir invariant) of the inhomogeneous group ISL(n,R) in its enveloping algebra is proposed, which using contractions of the tenso- rial indices of the generating…
To a finite quiver equipped with a positive integer on each of its vertices, we associate a holomorphic symplectic manifold having some parameters. This coincides with Nakajima's quiver variety with no stability parameter/framing if the…
Over a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation. In this paper, we employ a completely algebraic variation of…
This letter describes a novel derivation of general relativity by considering the (non)self-consistency of theories whose Hamiltonians are constraints. The constraints, from Hamilton's equations, generate the evolution, while the evolution,…
We generalize linear superalgebra to higher gradings and commutation factors, given by arbitrary abelian groups and bicharacters. Our central tool is an extension, to monoidal categories of modules, of the Nekludova-Scheunert faithful…
In this work we consider the class of Cayley graphs known as generalized Paley graphs (GP-graphs for short) given by $\Gamma(k,q) = Cay(\mathbb{F}_q, \{x^k : x\in \mathbb{F}_q^* \})$, where $\mathbb{F}_q$ is a finite field with $q$…
We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…
In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a…
We initiate a systematic study of non-planar on-shell diagrams in N=4 SYM and develop powerful technology for doing so. We introduce canonical variables generalizing face variables, which make the dlog form of the on-shell form explicit. We…
Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential…
For each natural number $n$, we consider the subgroup $\mathcal{R}_n$ of Homeo$_+[0,1]$ made by the elements that are linear except for a subset whose Cantor-Bendixson rank is less than or equal to $n$. These groups of generalized…
We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work by Edward Formanek, David Sibley, and Richard…
Bochner's theorem characterizes positive definite functions on groups through the positivity of their Fourier transforms and plays a fundamental role in Harmonic analysis. While Bochner-type results are known for certain classes of…
It is well known that for irreducible, square-integrable representations of a locally compact group, there exist so-called admissible vectors which allow the construction of generalized continuous wavelet transforms. In this paper we…
In this paper, we give a simple formula for sectional curvatures on the general linear group, which is also valid for many other matrix groups. Similar formula is given for a reductive Lie group. We also discuss the relation between…
We give a further extension and generalization of Dedekind's theorem over those presented by Yamaguchi. In addition, we give two corollaries on irreducible representations of finite groups and a conjugation of the group algebra of the…
Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron Frobenius-like theory for these matrices, obtaining three main results and drawing…