Related papers: Explicit reduction theory for SU(2,1;Z[i])

The covariant quantization of massless D=11 superparticle (M0-brane) in its twistor-like Lorentz harmonic formulation is used to clarify the origin and some properties of the Berkovits pure spinor approach to quantum superstring and to…

In D-dimensional spacetimes which can be foliated by n-dimensional homogeneous subspaces, a quantum field can be decomposed in terms of modes on the subspaces, reducing the system to a collection of (D-n)-dimensional fields. This allows one…

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…

The Gamma-class is a characteristic class for complex manifolds with transcendental coefficients. It defines an integral structure of quantum cohomology, or more precisely, an integral lattice in the space of flat sections of the quantum…

We consider the semi-direct products $G=\mathbb Z^2\rtimes GL_2(\mathbb Z), \mathbb Z^2\rtimes SL_2(\mathbb Z)$ and $\mathbb Z^2\rtimes\Gamma(2)$ (where $\Gamma(2)$ is the congruence subgroup of level 2). For each of them, we compute both…

We study the coadjoint representation of contractions of reductive Lie algebras associated with symmetric decompositions. Let $\frak g=\frak g_0\oplus \frak g_1$ be a symmetric decomposition of a reductive Lie algebra $\frak g$. Then the…

We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop…

Let $X$ be a negatively curved symmetric space and $\Gamma$ a non-cocompact lattice in $\rm{Isom}(X)$. We show that small, parabolic-preserving deformations of $\Gamma$ into the isometry group of any negatively curved symmetric space…

Cobordism offers a unique perspective into the non-perturbative sector of string theory by demanding the absence of higher form global symmetries for quantum gravitational consistency. In this work we compute the spin cobordism groups of…

Let $G = SO_0(2,m),$ the connected component of the Lie group $SO(2,m);\ K = SO(2) \times SO(m),$ a maximal compact subgroup of $G;$ and $\theta$ be the associated Cartan involution of $G.$ Let $X = G/K,\ \frak{g}_0$ be the Lie algebra of…

We provide several results on splice-quotient singularities: a combinatorial expression of the dimension of the first cohomology of all `natural' line bundles, an equivariant Campillo-Delgado-Gusein-Zade type formula about the dimension of…

We present reduction and reconstruction procedures for the solutions of symmetric stochastic differential equations, similar to those available for ordinary differential equations. Additionally, we use the local tangent-normal…

The spline space $C_k^r(\Delta)$ attached to a subdivided domain $\Delta$ of $\R^{d} $ is the vector space of functions of class $C^{r}$ which are polynomials of degree $\le k$ on each piece of this subdivision. Classical splines on planar…

Certain supergravity theories admit a remarkable consistent dimensional reduction in which the internal space is a sphere. Examples include type IIB supergravity reduced on S^5, and eleven-dimensional supergravity reduced on S^4 or S^7.…

In this paper, we describe the possible disconnected complex reductive algebraic groups $E$ with component group $\Gamma = E/E_0$. We show that there is a natural bijection between such groups $E$ and algebraic extensions of $\Gamma$ by…

Part I: The geometric algebra of space is derived by extending the real number system to include three mutually anticommuting square roots of plus one. The resulting geometric algebra is isomorphic to the algebra of complex 2x2 matrices,…

We describe a new type of discrete symmetry that relates heterotic-string models. It is based on the spectral flow operator which normally acts within a general N=(2,2) model and we use this operator to construct a map between N=(2,0)…

We consider spin system defined on the coadjoint orbit with noncompact symmetry and investigate the quantization. Classical spin with noncompact SU(N,1) symmetry is first formulated as a dynamical system and the constraint analysis is…

The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes,…

We introduce spin-harmonic structures, a class of geometric structures on Riemannian manifolds of low dimension which are defined by a harmonic unitary spinor. Such structures are related to SU(2) (dim=4,5), SU(3) (dim=6) and G_2 (dim=7)…