Related papers: Invariant functions on supermatrices

The groups mentioned in the title are certain matrix groups of infinite size over a finite field $\mathbb F_q$. They are built from finite classical groups and at the same time they are similar to reductive $p$-adic Lie groups. In the…

Let $M$ be a smooth manifold. When $\Gamma$ is a group acting on the manifold $M$ by diffeomorphisms one can define the $\Gamma$-co-invariant cohomology of $M$ to be the cohomology of the differential complex…

We prove that (GL_{2n}(C),Sp_{2n}(C)) is a Gelfand pair. More precisely, we show that for an irreducible smooth admissible Frechet representation (\pi,E) of GL_{2n}(C) the space of continuous functionals Hom_{Sp_{2n}(\cc)}(E,C) is at most…

Following the method already developed for studying the actions of GL_q(2,C) on the Clifford algebra C(1,3) and its quantum invariants (Commun. in Algebra 27, 1843-1878(1999)), we study the action on C(1,3) of the quantum group GL_2…

Let V be the space of 2x2x2 complex hypermatrices, endowed with the natural group action of GL=GL(2,C)^3. The category of GL-equivariant coherent D-modules on V is equivalent to the category of representations of a quiver with relations. In…

Gelfand duality between unital commutative C*-algebras and Compact Hausdorff spaces is extended to all unital C*-algebras, where the dual objects are what we call compact Hausdorff quantum spaces. We apply this result to obtain, a…

A series invariant for a certain class of closed 3-manifolds associated with a type I Lie superalgebra sl(m|n) was introduced recently. We find a q-series for the other Lie superalgebra of the same type of the minimum rank.

We study Sp(2n,R)-invariant functionals on the spaces of smooth vectors in Speh representations of GL(2n,R). For even n we give expressions for such invariant functionals using an explicit realization of the space of smooth vectors in the…

Let $G$ be a locally compact group. In this paper, we study various invariant subspaces of the duals of the algebras $A_M(G)$ and $A_{cb}(G)$ obtained by taking the closure of the Fourier algebra $A(G)$ in the multiplier algebra $MA(G)$ and…

For an operator $A$ on a complex Banach space $X$ and a closed subspace $M\subseteq X$, the local commutant of $A$ at $M$ is the set $C(A;M)$ of all operators $T$ on $X$ such that $TAx=ATx$ for every $x\in M$. It is clear that $ C(A;M)$ is…

We give a polynomial gluing construction of two groups $G_X\subseteq GL(\ell,\mathbb F)$ and $G_Y\subseteq GL(m,\mathbb F)$ which results in a group $G\subseteq GL(\ell+m,\mathbb F)$ whose ring of invariants is isomorphic to the tensor…

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the…

For a compact subgroup $G$ of the group of isometries acting on a Riemannian manifold $M$ we investigate subspaces of Besov and Triebel-Lizorkin type which are invariant with respect to the group action. Our main aim is to extend the…

Let $G$ be a subgroup of $S_n$, the symmetric group of degree $n$. For any field $k$, $G$ acts naturally on the rational function field $k(x_1,x_2,\ldots,x_n)$ via $k$-automorphisms defined by $\sigma\cdot x_i=x_{\sigma(i)}$ for any…

We study invariant theory of the general linear supergroup in positive characteristic. In particular, we determine when the symmetric group algebra acts faithfully on tensor superspace and demonstrate that the symmetric group does not…

Let $G$ be a Lie group acting on a vector space $V$. Given a set of $G$-invariants, one can ask the question : does this set of invariants characterize the group $G$ ? We recall here some known results, ask questions and state some…

We construct a bicovariant differential calculus on the quantum group $GL_q(3)$, and discuss its restriction to $[SU(3) \otimes U(1)]_q$. The $q$-algebra of Lie derivatives is found, as well as the Cartan-Maurer equations. All the…

We construct gauge invariant operators in non-commutative gauge theories which in the IR reduce to the usual operators of ordinary field theories (e.g. F^2). We show that in the deep UV the two-point functions of these operators admit a…

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…

The implications of N=1 superconformal symmetry for four dimensional quantum field theories are studied. Superconformal covariant expressions for two and three point functions of quasi-primary superfields of arbitrary spin are found and…