Related papers: On the global Gan-Gross-Prasad conjecture for gene…
The talk presents an ab initio construct of the spacetime structure underlying massive gravitinos. We argue that single spin interpretation of massive gravitino is untenable, and that a spin measurement in the rest frame for an unpolarized…
We consider faithful actions of simple algebraic groups on self-dual irreducible modules, and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the…
In this paper, we propose a conjectural multiplicity formula for general spherical varieties. For all the cases where a multiplicity formula has been proved, including Whittaker model, Gan-Gross-Prasad model, Ginzburg-Rallis model, Galois…
We prove algebraicity results for critical $L$-values attached to the group $\text{GSp}_4 \times \text{GL}_2$, and for Gan--Gross--Prasad periods which are conjecturally related to central $L$-values for $\text{GSp}_4 \times \text{GL}_2…
There are exactly three finite subgroups of SU(2) that act irreducibly in the spin 1 representation, namely the binary tetrahedral, binary octahedral and binary icosahedral groups. In previous papers I have shown how the binary tetrahedral…
The Green-Griffiths-Lang conjecture says that for every complex projective algebraic variety $X$ of general type there exists a proper algebraic subvariety of $X$ containing all nonconstant entire holomorphic curves $f:\mathbb{C} \to X$. We…
Studying two point branched Galois covers of the projective line we prove the Inertia Conjecture for the Alternating groups $A_{p+1}$, $A_{p+3}$, $A_{p+4}$ for any odd prime $p \equiv 2 \pmod{3}$ and for the group $A_{p+5}$ when…
The so called Gell-Mann or decontraction formula is proposed as an algebraic expression inverse to the Inonu-Wigner Lie algebra contraction. It is tailored to express the Lie algebra elements in terms of the corresponding contracted ones.…
We show that, in the weak field limit, at large separations, in sharp contrast to General Relativity (GR), all massive gravity theories predict distance-dependent spin alignments for spinning objects. For all separations GR requires…
We prove that if $G$ is the graph of a connected triangulated $(d-1)$-manifold, for $d\geq 3$, then $G$ is generically globally rigid in $\mathbb R^d$ if and only if it is $(d+1)$-connected and, if $d=3$, $G$ is not planar. The special case…
Let $\Sigma$ be a compact oriented surface. The Dehn twist along every simple closed curve $\gamma \subset \Sigma$ induces an automorphism of the fundamental group $\pi$ of $\Sigma$. There are two possible ways to generalize such…
We classify the pairs of group morphisms $\Gamma \rightarrow {\rm Spin}(7)$ which are element conjugate but not globally conjugate. As an application, we study the case where $\Gamma$ is the Weil group of a $p$-adic local field, which is…
As is well-known, the compact groups Spin(7) and SO(7) both have a single conjugacy class of compact subgroups of exceptional type G_2. We first show that if H is a subgroup of Spin(7), and if each element of H is conjugate to some element…
This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…
In this paper we study the Gan-Gross-Prasad problem for finite classical groups. Our results provide complete answers for unipotent representations, and we obtain the explicit branching laws for these representations. Moreover, for…
It has been known for some time that topological geons in quantum gravity may lead to a complete violation of the canonical spin-statistics relation : there may exist no connection between spin and statistics for a pair of geons. We present…
In general relativity the fermions are treated from the perspective of the gauged Lorentz group and by introducing the corresponding gauge fields the spin connection. This procedure is intimately related to the so-called "vielbein"…
This paper proves the branching laws for the full class of unitarizable representations of general linear groups in non-Archimedean local fields, extending the original notion of Gan-Gross-Prasad relevant pair for Arthur-type…
The main result of this short note is a generic version of Paz's conjecture on the lengths of generating sets in matrix algebras. Consider a generic g-tuple A=(A_1,..., A_g) of nxn matrices over a field. We show that whenever $g^{2d}\geq…
We consider effective theories with massive fields that have spins larger than or equal to two. We conjecture a universal cutoff scale on any such theory that depends on the lightest mass of such fields. This cutoff corresponds to the mass…