Related papers: Representation theoretic embedding of twisted Dira…

Suppose that $G$ is a locally compact group and $\pi$ is a (not necessarily irreducible) unitary representation of a closed normal subgroup $N$ of $G$ on a Hilbert space $H$. We extend results of Clifford and Mackey to determine when $\pi$…

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…

Let G be a connected simple linear Lie group and H in G a symmetric subgroup such that the corresponding symmetric space G/H is non-compactly causal. We show that any irreducible unitary representation of G leads naturally to a net of…

Let G be a real reductive Lie group with maximal compact sub- group K. We generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in case G and K do not have equal rank. We compute ordinary and twisted…

A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…

We study the action of a finite group on the Riemann-Roch space of certain divisors on a curve. If $G$ is a finite subgroup of the automorphism group of a projective curve $X$ over an algebraically closed field and $D$ is a divisor on $X$…

For a topological group G the intersection KO(G) of all kernels of ordinary representations is studied. We show that KO(G) is contained in the center of G if G is a connected pro-Lie group. The class KO(C) is determined explicitly if C is…

Let $G$ be a complex semisimple Lie group and ${G}_{\mathbb R}$ a real form that contains a compact Cartan subgroup $T_{\mathbb R}$. Let $\pi$ be a discrete series representation of $G_{\mathbb R}$. We present geometric interpretations in…

We consider the action of a real linear algebraic group $G$ on a smooth, real affine algebraic variety $M\subset \R^n$, and study the corresponding left regular $G$-representation on the Banach space $C_0(M)$ of continuous, complex valued…

Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.

This paper investigates some actions "\`a la Johnson" on the set, denoted by ${\cal E}$, of Spin-structures which are interpreted as special double-coverings of a trivial $S^1-$fibration over a non-orientable surface $N_{g+1}$. The group…

We study conformal $Spin$-subgeometry of submanifolds in a semi-Riemannian $Spin$-manifold, focusing on conformal $Spin$-manifolds $(M,[h])$ and their Poincar\'e-Einstein metrics $(X,g_+)$. Our approach is based on the spectral theory of…

Let X be a closed Riemannian manifold and let H\hookrightarrow X be an embedded hypersurface. Let X=X_+ \cup_H X_- be a decomposition of X into two manifolds with boundary, with X_+ \cap X_- = H. In this expository article, surgery -- or…

For a locally compact group $G$ we consider the algebra $CD(G)$ of convolution dominated operators on $L^{2}(G)$: An operator $A:L^2(G)\to L^2(G)$ is called convolution dominated if there exists $a\in L^1(G)$ such that for all $f \in…

For a simple real Lie group $G$ with Heisenberg parabolic subgroup $P$, we study the corresponding degenerate principal series representations. For a certain induction parameter the kernel of the conformally invariant system of second order…

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK\cap P are also discussed, where gK is a…

By a theorem of Mclean, the deformation space of an associative submanifold Y of an integrable G_2 manifold (M,\phi) can be identified with the kernel of a Dirac operator D:\Omega^{0}(\nu) -->\Omega^{0}(\nu) on the normal bundle \nu of Y.…

We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is…

If $G$ is a locally compact group, $CD(G)$ the algebra of convolution dominated operators on $L^2(G)$ then an important question is: Is $\mathbb{C}1+CD(G)$ (respectively $CD(G)$ if $G$ is discrete) inverse-closed in the bounded operators on…

If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then under the assumption that D is nonspecial, we compute a simplified formula for the trace of the natural representation…