Related papers: Triality in so(4,4), characteristic classes, D4 an…
In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL_2$ over a definite quaternion algebra $D/\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having…
We describe all the fine group gradings, up to equivalence, on the Lie algebra $\mathfrak d_4$. This problem is equivalent to finding the maximal abelian diagonalizable subgroups of the automorphism group of $\mathfrak d_4$. We prove that…
The trialitarian automorphisms considered in this paper are the outer automorphisms of order 3 of adjoint classical groups of type D_4 over arbitrary fields. A one-to-one correspondence is established between their conjugacy classes and…
We give a detailed description of the algebraic group Aut(g) of automorphisms of a simple finite dimensional Lie superalgebra g over an algebraically closed field k of characteristic 0. We also give a description of the group of…
Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin(8) triality automorphisms. Different signature versions of theories such as 10-dimensional SYM's, superstrings, five-branes, F-theory,…
We classify the solvable subalgebras, semisimple subalgebras, and Levi decomposable subalgebras of $\mathfrak{so}(4,\mathbb{C})$, up to inner automorphism. By Levi's Theorem, this is a full classification of the subalgebras of…
In \cite[Section 5, p.32]{Arnold-1998}, Arnold writes: "Classification of singularities of curves can be interpreted in dual terms as a description of 'co-artin' subalgebras of finite co-dimension in the algebra of formal series in a single…
Working over an arbitrary base scheme, we provide an alternative development of triality which does not use Octonion algebras or symmetric composition algebras. Instead, we use the Clifford algebra of the split hyperbolic quadratic form of…
A theory of characteristic classes of vector bundles and smooth manifolds plays an important role in the theory of smooth manifolds. An investigation of reasonable notions of characteristic classes of singular spaces started since a…
We investigate the graded Lie algebras of Cartan type $W$, $S$ and $H$ in characteristic 2 and determine their simple constituents and some exceptional isomorphisms between them. We also consider the graded Lie algebras of Cartan type $K$…
The split quartic Cayley algebra is a structurable algebra which has been used to give constructions of Lie algebras of type D4. Here, we calculate its group of automorphisms, its algebra of derivations and its gradings.
Through the triality of ${\rm SO}(8,\mathbb{C})$, we study three interrelated homogeneous basis of the ring of invariant polynomials of Lie algebras, which give the basis of three Hitchin fibrations, and identify the explicit automorphisms…
We give a review of recent works for non-associative algebras, especially Lie algebras satisfying the triality relation. They are also intimately related to S_4 (symmetric group of 4-objects) symmetry of the Lie algebras.
This paper explores the moduli-dependent coefficients of higher derivative interactions that appear in the low-energy expansion of the four-graviton amplitude of maximally supersymmetric string theory compactified on a d-torus. These…
Representations of $\text{SO}(4,2)$ are constructed using $4\times4$ and $2\times2$ matrices with elements in $\mathbb{H}'\otimes\mathbb{C}$, and the known isomorphism between the conformal group and $\text{SO}(4,2)$ is written explicitly…
We prove the classification of discrete automorphic representations of GSp$_4$ explained in [Art04], as well as a compatibility between the local Langlands correspondences for GSp$_4$ and Sp$_4$ .
If G is a (connected) complex Lie Group and Z is a generalized flag manifold for G, the the open orbits D of a (connected) real form G_0 of G form an interesting class of complex homogeneous spaces, which play an important role in the…
Triality is a classical notion in geometry that arose in the context of the Lie groups of type $D_4$. Another notion of triality, Wilson triality, appears in the context of reflexible maps. We build a bridge between these two notions,…
We will consider a two dimensional "symmetric" subfamily of the four dimensional family of Fricke cubic surfaces. The main result is that such symmetric cubic surfaces arise as character varieties for the exceptional group of type G_2.…
While electromagnetic duality is a symmetry of many supergravity theories, this is not the case for the N=8 gauged theory. It was recently shown that this rotation leads to a one-parameter family of SO(8) supergravities. It is an open…