Related papers: Spinorial Representations of Orthogonal Groups

In this paper, we construct a version of orthogonal calculus for functors from $C_2$-representations to $C_2$-spaces, where $C_2$ is the cyclic group of order 2. For example, the functor $BO(-)$, that sends a $C_2$-representation to the…

We determine the Stiefel-Whitney classes of the second exterior representation and the spin representation of Spin(15), which are useful to calculate the mod 2 cohomology of the classifying space of the exceptional Lie group E_8.

We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…

First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…

Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $\Sigma$ of genus $l >1$, the order of the group $H^2(\Sigma,\pi_1(G))$ is equal to the number of connected components of the…

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

Let $G$ be a connected, simply connected nilpotent group and $\pi$ be a square-integrable irreducible unitary representation modulo its center $Z(G)$ on $L^2(\mathbf{R}^d)$. We prove that under reasonably weak conditions on $G$ and $\pi$…

Let $G_n$ denote either the group $Sp(2n, F)$ or $SO(2n+1, F)$ over a non-archimedean local field $F$. We determine the composition series of representations of $G_n$ induced from cuspidal and ladder representations such that the minimal…

Let $G$ be a special $p$-group. If $G$ is of rank two, or $G$ is of maximum rank with $|G^p|\leq p$, then we describe the complex irreducible projective representations of $G$.

Let $q$ be an odd prime power, and $G=\text{Sp}(2n,q)$ the finite symplectic group. We give an expression for the total Stiefel-Whitney Classes (SWCs) for orthogonal representations $\pi$ of $G$, in terms of character values of $\pi$ at…

In this thesis, we construct a new version of orthogonal calculus for functors $F$ from $C_2$-representations to $C_2$-spaces, where $C_2$ is the cyclic group of order 2. For example, the functor $BO(-)$, which sends a $C_2$-representation…

This paper provides a comparison between the $K$-structure of unipotent representations and regular sections of bundles on nilpotent orbits for complex groups of type $D$. Precisely, let $ G_ 0 =Spin(2n,\mathbb C)$ be the Spin complex group…

This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra…

We generalize the concept of cubic group into any dimension and derive their conjugate classifications and representation theorys. Double group and spinor representation are defined. A detailed calculation is carried out on the structures…

We compute explicitly the group of connected components $\pi_0G(\mathbb{R})$ of the real Lie group $G(\mathbb{R})$ for an arbitrary (not necessarily linear) connected algebraic group $G$ defined over the field $\mathbb{R}$ of real numbers.…

Hypercubic groups in any dimension are defined and their conjugate classifications and representation theories are derived. Double group and spinor representation are introduced. A detailed calculation is carried out on the structures of…

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations…

In this paper we give a classification of the $H$-spherical unitary highest weight representations of a hermitian Lie group $G$.

We survey different tools to classify representations of compact Lie groups according to their cohomogeneity and apply these methods to the case of irreducible representations of cohomogeneity 6, 7 and 8.

The special linear representation of a compact Lie group G is a kind of linear representation of compact Lie group G with special properties. It is possible to define the integral of linear representation and extend this concept to special…