Related papers: On Linear Representation, Complexity and Inversion…
Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (c) sesquilinear…
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
Memoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they typically involve…
The linear representation hypothesis is the informal idea that semantic concepts are encoded as linear directions in the representation spaces of large language models (LLMs). Previous work has shown how to make this notion precise for…
In recent years, deep learning-based sequence modelings, such as language models, have received much attention and success, which pushes researchers to explore the possibility of transforming non-sequential problems into a sequential form.…
We prove that if M is a vertically 4-connected matroid with a modular flat X of rank at least three, then every representation of M | X over a finite field F extends to a unique F-representation of M. A corollary is that when F has order q,…
The sets ${\Phi({F}^{\mu \nu})}, {\Phi(\tilde {F}^{\mu \nu})}$ of linear functionals on the space $< F,+,\cdot >$ represent themself linear space $< \Phi,+,\cdot >$ over the field of \textit{scalars} $P$, which is dual to space $< F,+,\cdot…
A group is called matricial field (MF) if it admits finite dimensional approximate unitary representations which are approximately faithful and approximately contained in the left regular representation. This paper provides a new class of…
We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which `functional representations' of particular hierarchies (like KP, discrete KP, mKP, AKNS), i.e. formulations in terms of…
For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actions on the twisted homology of associated spaces; these are…
We give a complete list of indecomposable characters of the infinite symmetric semigroup. In comparison with the analogous list for the infinite symmetric group, one should introduce only one new parameter, which has a clear combinatorial…
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
In this paper we study the Frobenius characters of the invariant subspaces of the tensor powers of a representation V. The main result is a formula for these characters for a polynomial functor of V involving the characters for V. The main…
As an attempt to give an unified description of quark and lepton mass matrices M_f, the following mass matrix form is proposed: the form of the mass matrices are invariant under a cyclic permutation (f_1 \to f_2, f_2 \to f_3, f_3 \to f_1)…
We use pluriharmonic maps to study representations of fundamental groups of algebraic manifolds. This approach is functorial in the sense that the restriction of such a map to a fiber of a fibration remains pluriharmonic, and on this basis,…
Finite (or Discrete) Fourier Transforms (FFT) are essential tools in engineering disciplines based on signal transmission, which is the case in most of them. FFT are related with circulant matrices, which can be viewed as group matrices of…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
It is well-known that characters classify linear representations of finite groups, that is if characters of two representations of a finite group are the same, these representations are equivalent. It is also well-known that, in general,…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
We propose graph theoretic equivalents for existence of a finite projective plane. We then develop a new approach and see that the problem of existence of a finite projective plane of order n is linked up with a subset of sharply 2…