Related papers: Real double coset spaces and their invariants

We define the equivariant degree and local degree of a proper $G$-equivariant map between smooth $G$-manifolds when $G$ is a compact Lie group and prove a local to global result. We show the local degree can be used to compute the…

Let F be a non Archimedean locally compact field of residue characteristic different from 2, let G be a connected reductive group defined over F, let s be an involutive F-automorphism of G and H an open F-subgroup of the fixed points group…

It is proved that, under certain restrictions on weights, a pair of weighted Hardy spaces on the two-dimensional torus is K-closed in the pair of the corresponding weighted Lebesgue spaces. By now, K-closedness of Hardy spaces on the…

We express the genus-two fixed-complex-structure enumerative invariants of P^2 and P^3 in terms of the genus-zero enumerative invariants. The approach is to relate each genus-two fixed-complex-structure enumerative invariant to the…

Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever…

Let $G/H$ be a reductive symmetric space of split rank $1$ and let $K$ be a maximal compact subgroup of $G$. In a previous article the first two authors introduced a notion of cusp forms for $G/H$. We show that the space of cusp forms…

In this paper we answer two long-standing questions in the classification of $G$-torsors on curves for an almost simple, simply connected algebraic group $G$ over the field of complex numbers. The first question is to give an intrinsic…

We present a systematic framework for constructing consistent truncations of supergravity based on exceptional generalized cosets of the form $\GS \backslash G/H$. This approach generalizes the well-established generalized Scherk-Schwarz…

We use recent progress on Chern-Simons gauge theory in three dimensions [18] to give explicit, closed form formulas for the star product on some functions on the affine space ${\mathcal A}(\Sigma)$ of (smooth) connections on the trivialized…

In previous work, the second author and others have found conditions on a homogeneous space $G/H$ which imply that, up to stabilization, all vector bundles over $G/H$ admit Riemannian metrics of non-negative sectional curvature. One…

We study the twisted K-theory and K-homology of some infinite dimensional spaces, like SU(\infty), in the bivariant setting. Using a general procedure due to Cuntz we construct a bivariant K-theory on the category of separable…

A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…

A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming…

We study the fixed points of the universal G-equivariant n-dimensional complex vector bundle and obtain a decomposition formula in terms of twisted equivariant universal complex vector bundles of smaller dimension. We use this decomposition…

Let $G$ be a split (minimal) Kac-Moody group over $\mathbb{R}$ or $\mathbb{C}$ with maximal torus $T$, and let $\theta$ be a Cartan-Chevalley involution of $G$, twisted by complex conjugation, and satisfying that $\theta(T)=T$. Furthermore,…

For a second countable locally compact group $G$ and a closed abelian subgroup $H$, we give a range function classification of closed subspaces in $L^2(G)$ invariant under left translation by $H$. For a family $\mathscr{A} \subset L^2(G)$,…

Let $G$ be a connected complex Lie group. A real form of $G$ is a closed subgroup $H\subset G$ whose Lie algebra $\mathfrak{h}$ is a real form of the Lie algebra $\mathfrak{g}$ of $G$. A pair $(G,H)$ of this type is reductive, and the…

Inspired by group cohomology, we define several coarse topological invariants of metric spaces. We define the coarse cohomological dimension of a metric space, and demonstrate that if G is a countable group, then the coarse cohomological…

A rich pattern of gauge symmetries is found in the moduli space of heterotic string toroidal compactifications, at fixed points of the T-duality transformations. We analyze this pattern for generic tori, and scrutinize in full detail…

Worldsheet (0,2) gauged linear sigma models are often used to study supersymmetric heterotic string compactifications with non-trivial vector bundles. We make use of supersymmetric localization techniques to determine their one-loop…