Related papers: Majorana Algebra for the Hoffman-Singleton Graph

The Riemann-Hilbert approach to studying solutions of supergravity theories allows us to associate spacetime independent monodromy matrices (matrices in the Geroch group) with solutions that effectively only depend on two spacetime…

Majorana-Weyl spacetimes offer a rich algebraic setup and new types of space-time dualities besides those discussed by Hull. The triality automorphisms of Spin(8) act non-trivially on Majorana-Weyl representations and Majorana-Weyl…

The algebraic Joker module was originally described in the 1970s by Adams and Priddy and is a $5$-dimensional module over the subHopf algebra $\mathcal{A}(1)$ of the mod $2$ Steenrod algebra. It is a self-dual endotrivial module, i.e., an…

Consider a compact locally symmetric space $M$ of rank $r$, with fundamental group $\Gamma$. The von Neumann algebra $\vn(\Gamma)$ is the convolution algebra of functions $f\in\ell_2(\Gamma)$ which act by left convolution on…

Majorana fermions (MFs) in a topological superconductor exhibit anisotropic electromagnetic responses, called Majorana multipole responses, when MFs are degenerate under time-reversal and crystalline symmetries. In time-reversal symmetric…

We describe the set of generalized Poincare and conformal superalgebras in D=4,5 and 7 dimensions as two sequences of superalgebraic structures, taking values in the division algebras R, C and H. The generalized conformal superalgebras are…

We study some arithmetic properties of the mirror maps and the quantum Yukawa coupling for some 1-parameter deformations of Calabi-Yau manifolds. First we use the Schwarzian differential equation, which we derived previously, to…

We study the solutions of generic Hamiltonians exhibiting particle-hole mixing. We show that there exists a universal quantity that can describe locally the Majorana nature of a given state. This pseudo-spin like two-component quantity is…

Topological terms in the O(3) nonlinear sigma model in (1+1) and (2+1) dimensions are re-examined based on the description of the SU(2)-valued field $g$. We first show that the topological soliton term in (1+1) dimensions arises from the…

Let $D$ be the incidence graph of the projective plane over $\FF_3$. The Artin group of the graph $D$ maps onto the bimonster and a complex hyperbolic reflection group $\Gamma$ acting on 13 dimensional complex hyperbolic space $Y$. The…

We present a new construction of four dimensional $\mathcal N=3$ theories, given by M5 branes wrapping a $T^2$ in an M-theory U-fold background. The resulting setup generalizes the one used in the usual class $\mathcal S$ construction of…

We develop a framework for displaying the stable homotopy theory of the sphere, at least after localization at the second Morava K-theory K(2). At the prime 3, we write the spectrum L_{K(2)S^0 as the inverse limit of a tower of fibrations…

Topological crystalline superconductors are known to have possible higher-order topology, which results in Majorana modes on $d-2$ or lower-dimensional boundaries. Given the rich possibilities of boundary signatures, it is desirable to have…

If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the…

We propose a gravitational response theory for point defects (hedgehogs) binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in 4+1 dimensions, where the point defect is extended into a line, a coupling of the bulk…

The faces of the braid arrangement form a monoid. The associated monoid algebra -- the face algebra -- is well-studied, especially in relation to card shuffling and other Markov chains. In this paper, we explore the action of the symmetric…

If the holonomy representation of an $(n+2)$--dimensional simply-connected Lorentzian manifold $(M,h)$ admits a degenerate invariant subspace its holonomy group is contained in the parabolic group $(\mathbb{R} \times SO(n))\ltimes…

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…

If A is a weak C^*-Hopf algebra then the category of finite dimensional unitary representations of A is a monoidal C^*-category with monoidal unit being the GNS representation D_eps associated to the counit \eps. This category has…

For a finite subgroup $G$ of the special unitary group $SU_2$, we study the centralizer algebra $Z_k(G) = End_G(V^{\otimes k})$ of $G$ acting on the $k$-fold tensor product of its defining representation $V= \mathbb{C}^2$. These subgroups…