Related papers: Gauss decomposition for Chevalley groups, revisite…

The decays tau -> 3 pi + nu(tau) are analyzed at one loop order in the framework of Generalized Chiral Perturbation Theory, in order to test the sensitivity to the size of spontaneous chiral symmetry breaking parameters, contained in the…

We describe a refinement of the general theory of higher rank Euler, Kolyvagin and Stark systems in the setting of the multiplicative group over arbitrary number fields. We use the refined theory to prove new results concerning the Galois…

Let $\Phi$ be a reduced irreducible root system of rank $\ge 2$, let $R$ be a commutative ring and let $I,J$ be two ideals of $R$. In the present paper we describe generators of the commutator groups of relative elementary subgroups…

We continue study of subgroups of a Chevalley group $G_P(\Phi,R)$ over a ring $R$ with a root system $\Phi$ and a weight lattice $P$, containing the elementary subgroup $E_P(\Phi,K)$ over a subring $K$ of $R$. Recently A. Bak and A.…

In studying the structure of derived categories of module categories of group algebras or their blocks, it is fundamental to classify support $\tau$-tilting modules. Koshio and Kozakai showed that the structure of support $\tau$-tilting…

We prove a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X//G for…

In [4], we use the root categories to realize Chevalley groups. Lusztig's theory of total positivity for reductive groups can be naturally applied to Chevalley groups. In this paper, we explicitly determine regions of $\mathbb{R}_{>0}^t$…

We establish some interactions between uniformly recurrent subgroups (URSs) of a group $G$ and cosets topologies $\tau_\mathcal{N}$ on $G$ associated to a family $\mathcal{N}$ of normal subgroups of $G$. We show that when $\mathcal{N}$…

Prior work [arXiv:2106.16248] shows that the Standard Model (SM) naturally arises near a gapless quantum critical region between Georgi-Glashow (GG) $su(5)$ and Pati-Salam (PS) $su(4) \times su(2) \times su(2)$ models of quantum vacua (in a…

Let $G$ be a semisimple Lie group with a maximal torus $T$. We present an explicit formula for the Borel transgression $\tau :H^{1}(T)\rightarrow H^{2}(G/T)$ of the fibration $G\rightarrow G/T$. This formula corrects an error in the paper…

We discuss semileptonic and leptonic B decays, B to D^{(*)} tau nu and B to tau nu, in the chiral U(1)' models which were proposed by the present authors in the context of the top forward-backward asymmetry (A^t_FB) observed at the…

If $G$ is a compact connected Lie group and $T$ is a maximal torus, we give a wedge decomposition of $\Sigma G/T$ by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of $G/T$.

We disprove a strong form of the Regular Inverse Galois Problem: there exist finite groups $G$ which do not have a realization $F/\Qq(T)$ that induces all Galois extensions $L/\Qq(U)$ of group $G$ by specializing $T$ to $f(U) \in \Qq(U)$.…

Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that the invariant ring $U^G$ is also…

Let G be a reductive group over a commutative ring R. We say that G has isotropic rank >=n, if every normal semisimple reductive R-subgroup of G contains (G_m)^n. We prove that if G has isotropic rank >=1 and R is a regular domain…

Suppose G is a real reductive Lie group in Harish-Chandra's class. We propose here a structure for the set \Pi_u(G) of equivalence classes of irreducible unitary representations of G. (The subscript u will be used throughout to indicate…

Let $k$ be a perfect field. Assume that the characteristic of $k$ satisfies certain tameness assumptions \eqref{tameness}. Let $\mathcal O_{_n} := k\llbracket z_{_1}, \ldots, z_{_n}\rrbracket$ and set $K_{_n} := \text{Fract}~\cO_{_n}$. Let…

We investigate whether a spontaneously-broken gauge theory of the group $SU(2,2)$ may be a genuine competitor to General Relativity. The basic ingredients of the theory are an $SU(2,2)$ gauge field $A_{\mu}$ and a Higgs field $W$ in the…

We propose that the structure of gauge theories, the $(2,0)$ and little-string theories is encoded in a unique function on the real group manifold $E_{10}(R)$. The function is invariant under the maximal compact subgroup $K$ acting on the…

We give explicit formulas for torus-equivariant fundamental classes of closed $K$-orbits on the flag variety $G/B$ when $G$ is one of the classical groups $SL(n,\C)$, $SO(n,\C)$, or $Sp(2n,\C)$, and $K$ is a symmetric subgroup of $G$. We…