Related papers: On covariant functions and distributions under the…

Let the finite group $G$ act linearly on the vector space $V$ over the field $k$ of arbitrary characteristic. If $H<G$ is a subgroup the extension of invariant rings $k[V]^G\subset k[V]^H$ is studied using modules of covariants. An example…

We prove a reduced version of the Chevalley restriction conjecture on the commuting scheme posed by T.H. Chen and B.C. Ng\^o, extending the results of Hunziker for classical groups. In particular, we prove that for any connected reductive…

We give a general formula for the equivariant complex $K$-theory $K_G^*(V)$ of a finite dimensional real linear space $V$ equipped with a linear action of a compact group $G$ in terms of the representation theory of a certain double cover…

Symmetry plays a basic role in variational problems (settled e.g. in $\mathbb R^{n}$ or in a more general manifold), for example to deal with the lack of compactness which naturally appear when the problem is invariant under the action of a…

Let $M$ be a commutative homogeneous space of a compact Lie group $G$ and $A$ be a closed $G$-invariant subalgebra of the Banach algebra $C(M)$. A function algebra is called antisymmetric if it does not contain nonconstant real functions.…

Let $F$ be a nonarchimedean local field, and $G$ the group of $F$-points of a c onnected quasisplit reductive group defined on $F$; in this paper, we will study the distributions on $G$ which are invariant by conjugation, and the vector spa…

Let G be a finite group acting tamely on a proper reduced curve C over an algebraically closed field. We study the G-module structure on the cohomology groups of a G-equivariant locally free sheaf F on C, and give formulas of…

We consider a finite dimensional $\kk G$-module $V$ of a $p$-group $G$ over a field $\kk$ of characteristic $p$. We describe a generating set for the corresponding Hilbert Ideal. In case $G$ is cyclic this yields that the algebra $\kk[V]_G$…

An invariant random subgroup $H \leq G$ is a random closed subgroup whose law is invariant to conjugation by all elements of $G$. When $G$ is locally compact and second countable, we show that for every invariant random subgroup $H \leq G$…

Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…

Let $W$ be a finite reflection group. A $W$-invariant function of class~$C^{\infty}$ may be expressed as a functions of class $C^{\infty}$ of the basic invariants. In finite class of differentiability, the situation is not this simple.…

Let $N\unlhd G$ be a pair of finite subgroups of $\mathrm{SL}_2(\mathbb{C})$ and $V$ a finite-dimensional fundamental $G$-module. We study Kostant's generating functions for the decomposition of the $\mathrm{SL}_2(\mathbb C)$-module…

We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. Let G be a compact quantum group, and let T:= Rep(G) be the rigid C*-tensor category of finite-dimensional continuous unitary representations of G. Let…

If $G$ is a finite group, the Grothendieck group ${\mathbf{K}}\_G(G)$ of the category of $G$-equivariant ${\mathbb{C}}$-vector bundles on $G$ (for the action of $G$ on itself by conjugation) is endowed with a structure of (commutative)…

A theorem of Gerald Schwarz [24, Thm. 1] says that for a linear action of a compact Lie group $G$ on a finite dimensional real vector space $V$ any smooth $G$-invariant function on $V$ can be written as a composite with the Hilbert map. We…

If G is a Lie group, let D(G) be the space of compactly supported smooth functions on G. Consider the bilinear map B : D(G) x D(G) -> D(G), (f,g) |-> f*g which takes a pair of test functions to their convolution. We show that B is…

Let $c:\mathcal{G}\to\R$ be a cocycle on a locally compact Hausdorff groupoid $\mathcal{G}$ with Haar system. Under some mild conditions (satisfied by all integer valued cocycles on \'{e}tale groupoids), $c$ gives rise to an unbounded odd…

In the paper, it is proved that any $C^{1}$-function on GL(n) which is locally $P$-invariant (here $P$ is the affine (sub)group of GL(n)) is locally $G$-invairant. There is also a statement for distributions (a very weak form of Baruch's…

Let G be the group of points of a split reductive algebraic group over a local field k and let X=G/U where U is a maximal unipotent subgroup of G. In this paper we construct certain canonical G-invariant space S(X) (called the Schwartz…

In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…