Related papers: Super invariant theory in positive characteristic
A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this paper. This is done by walking through the most important cases…
We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…
We prove a few basic facts about the space of bi-invariant (or left-invariant) total order relations on a torsion-free, nonabelian, nilpotent group G. For instance, we show that the space of bi-invariant orders has no isolated points (so it…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
The fundamental representations of the special linear group ${\rm SL}_n$ over the complex numbers are the exterior powers of $\mathbb{C}^n$. We consider the invariant rings of sums of arbitrary many copies of these ${\rm SL}_n$-modules. The…
We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.
We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…
We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the…
We define the notion of characteristic classes for supermanifolds endowed with a homological vector field $Q$. These take values in the cohomology of the Lie derivative operator $L_Q$ acting on arbitrary tensor fields. We formulate a…
Starting with a supersymmetric U(N)xU(N) gauge theory built in N=1 superspace, a nonsupersymmetric theory is obtained by ``twisting'' the gauginos into a different representation of the group than the gauge bosons. Despite the fact that…
Working over an algebraically closed base field $k$ of characteristic 2, the ring of invariants $R^G$ is studied, where $G$ is the orthogonal group O(n) or the special orthogonal group SO(n), acting naturally on the coordinate ring $R$ of…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two…
We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…
In this note we generalize several well known results concerning invariants of finite groups from characteristic zero to positive characteristic not dividing the group order. The first is Schmid's relative version of Noether's theorem. That…
We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.
The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain…
The classical action of a two dimensional N=2 supersymmetric theory, characterized by a general K\"{a}hler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant…
We introduce the quantum $j$-invariant in positive characteristic as a multi-valued, modular-invariant function of a local function field. In this paper, we concentrate on basic definitions and questions of convergence. Note: This version…