On extended Weil representation for finite general linear group and Howe correspondenceWeil representations of general linear groupsEtale cohomology of affine varietiesFourier transformLet q be a power of a prime number. We construct a variety over a finite field F-q and show that its middle ...
A (linear) representation of G in V is a homomorphism ρ:G→GL(V) , where GL(V) is the group of linear isomorphisms of V. Then ρ defines a (linear) action of G on V. In fact, 1x=idVx=x,g(hx)=ρ(g)(ρ(h)x)=ρ(g)∘ρ(h)(x)=ρ(gh)(x)=(gh)x and g(x+y...
For the general linear group $GL_n(k)$ over an algebraically closed field $k$ of characteristic $p$, there are two types of "twisting" operations that arise naturally on partitions. These are of the form $\\\lambda ightarrow p\\\lambda$ and $\\\lambda ightarrow \\\lambda + p^rau...
(i)x_1\cdot x_2\,\,is\,\,linear\,\,in\,\,each\,\,of\,\,the\,\,variables\,\,x_1\,\,and\,\,x_2.\\(ii)If\,\,(e_{i_1})\,\,is\,\,a\,\,basis\,\,of\,\,V_1\,\,and\,\,(e_{i_2})\,\,is\,\,a\,\,basis\,\,of\,\,V_2,the\,\,family\,\,of\,...
linear transport problemdispersion relationsnormalization coefficientseigenfunctions/ A0380 General theory of scattering A0560 Transport processes: theoryThe spectral representation of the linear transport problem is applied to two additional examples. In the first example, we obtain the dispersion relations, ...
Recently, the extension and inversion of T : X → X for more general X has been studied in [6], where it is shown that there exists a larger space [T, X], optimal in a well defined sense, which contains X continuously and such that T can be extended to a continuous linear ...
Clausen, M.: Letter Place Algebras and a Characteristic-Free Approach to the Representation Theory of the General Linear and Symmetric Groups, I. Adv. Math. 33, 161–191 (1979) CrossRef Doubilet, P., Rota, G.-C., Stein, J.: On the foundation of combinatorial theory IX. Combinatoria...
Wagner, M. Weller, Linear algebra over small finite fields on parallel machines, Vorlesungen Fachbereich Mathematik Universitat GH Essen, Heft 23 (1995). H. W. GoHan, The 5-modular representations of the Tits simple group, Math. Compo 57(1991), 369–386. H. W. GoHan, A new existence ...
TorusE defines the principle of TransE on Lie group. A torus, which is one of the compact Lie groups, can be chosen for the embedding space to avoid regularization. TorusE is the first model that embeds objects on other than a real or complex vector space, and this paper is the first ...
This vector is said to carry the irreducible representation of the SO(3) group of dimension 2l + 1. If the input vectors are transformed according to Eq. (2), then all the internal features and the output vectors of the ENN will also be transformed accordingly. Under this constraint,...