Related papers: The octic E8 invariant
We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal (T) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized in one…
In this paper, we classify all unitary representations with non-zero Dirac cohomology for complex Lie group of Type E8. This completes the classification of Dirac series for all complex simple Lie groups.
Making use of the SO(3,1) Lorentz algebra, we derive in this paper two series of Gauss-Bonnet type identities involving torsion, one being of the Pontryagin type and the other of the Euler type. Two of the six identities involve only…
By constructing concrete complex-oriented maps we show that the eight-fold of the generator of the third integral cohomology of the spin groups Spin(7) and Spin(8) is in the image of the Thom morphism from complex cobordism to singular…
Let G be a group of order 8 and F an algebraically closed field with char= 2. In this paper we compute the number of n degree representations of G and subsequent dimensions of the corresponding spaces of invatiant bilinear forms over the…
In 1994, Witten has defined a monopole invariant and he has shown the equivalence of this invariant with Donaldson's polynomial using his result in \( \SS \)-duality. This new invariant is very powerful because the gauge group is abelian.…
We are presenting an algorithm capable of simplifying tensor polynomials with indices when the building tensors have index symmetry properties. These properties include simple symmetry, cyclicity and those due to the presence of covariant…
About 6 years ago, semitoric systems were classified by Pelayo & Vu Ngoc by means of five invariants. Standard examples are the coupled spin oscillator on $\mathbb{S}^2 \times \mathbb{R}^2$ and coupled angular momenta on $\mathbb{S}^2…
The Ehrhart polynomial and the reciprocity theorems by Ehrhart \& Macdonald are extended to tensor valuations on lattice polytopes. A complete classification is established of tensor valuations of rank up to eight that are equivariant with…
Motivated by the Turaev-Viro invariant of 3-manifolds, we construct a formal topological invariant of closed, oriented 3-manifolds involving spherical tetrahedra as an application of the asymptotic formula of 6j symbols for the Quantum…
In the present paper we set up a connection between the indices of the Tits algebras of a simple linear algebraic group $G$ and the degree one parameters of its motivic $J$-invariant. Our main technical tool are the second Chern class map…
We identify a new symmetry for the equations governing odderon amplitudes, corresponding in the Regge limit of QCD to the exchange of 3 reggeized gluons. The symmetry is a modular invariance with respect to the unique normal subgroup of…
Using the Rost invariant for torsors under Spin groups one may define an analogue of the Arason invariant for certain hermitian forms and orthogonal involutions. We calculate this invariant explicitly in various cases, and use it to…
Let $p$ be an odd prime and $\mathbb{F}_p$ be the prime field of order $p$. Consider a $2$-dimensional orthogonal group $G$ over $\mathbb{F}_p$ acting on the standard representation $V$ and the dual space $V^*$. We compute the invariant…
To an orthogonal or unitary involution on a central simple algebra of degree 4, or to a symplectic involution on a central simple algebra of degree 8, we associate a Pfister form that characterises the decomposability of the algebra with…
Given an odd prime $p$, we identify composition factors of the reduction modulo $p$ of spin irreducible representations of the covering groups of symmetric groups indexed by partitions with 2 parts and find some decomposition numbers.
We give two equivalent sets of invariants which classify pairs of coisotropic subspaces of finite-dimensional Poisson vector spaces. For this it is convenient to dualize; we work with pairs of isotropic subspaces of presymplectic vector…
A new matrix model is described, based on the exceptional Jordan algebra. The action is cubic, as in matrix Chern-Simons theory. We describe a compactification that, we argue, reproduces, at the one loop level, an octonionic…
We provide a simple presentation by generators and relations of the ring of $\omega$-invariant symmetric functions over the field $\mathbb{F}_{2}$. Here, $\omega$ denotes the standard involution on the ring of symmetric functions,…
In a previous paper, the BRST cohomology in the pure spinor formalism of the superstring was shown to coincide with the light-cone Green-Schwarz spectrum by using an SO(8) parameterization of the pure spinor. In this paper, the SO(9,1)…