Related papers: Functoriality for General Spin Groups
We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…
The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence…
We study the Picard groups of connected linear algebraic groups, and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every global function field. We also utilize our study of these…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…
In this article we prove various results about transferring or lifting $\mathrm{A}_\infty$-algebra structures along quasi-isomorphisms over a commutative ring.
In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for general semisimple algebraic group $G$ defined over a number field $k$ such that its Archimedean…
We study $t$-designs of parameters $(n,k,\lambda)$ over finite fields as group divisible designs and set systems admitting a transitive action of a linear group encoded in an hypergraph $G$ whose vertex set of size $n$ is partitioned into…
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the…
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
Let $G$ be a split simply-connected group of type $D$ or $E$. The minimal automorphic representation $\Pi$ of $G(\mathbb A)$ admits a realization on a space of functions $\mathcal S(X(\mathbb A))$ for a variety $X$. In this paper we write…
A general framework of constructions of endoscopy correspondences via automorphic integral transforms for classical groups is formulated in terms of the Arthur classification of the discrete spectrum of square-integrable automorphic forms.…
Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum…
Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in Quantum Field Theory. This representation permutes ``Gaussian'' elements in the fermion Fock space, and is necessarily projective:…
Let $F$ be a $p$-adic field, and $G_n$ one of the groups $GL(n,F)$, $GSO(2n-1,F)$, $GSp(2n,F)$, or $GSO(2(n-1),F)$. Using the mirabolic subgroup or analogues of it, and related "derivative" functors, we give an asymptotic expansion of…
Spinorial methods have proven to be a powerful tool to study geometric properties of spin manifolds. Our aim is to continue the spinorial study of manifolds that are not necessarily spin. We introduce and study the notion of $G$-invariance…
The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The…
We derive the spin-statistics theorem in both relativistic and non-relativistic first-quantized form, extending considerably the earlier proofs. Our derivation is based on the representation theories of the groups SU (2) and SL(2,C), latter…
Among all affine, flat, finitely presented group schemes, we focus on those that are pure, this includes all groups which are extensions of a finite locally free group by a group with connected fibres. We prove that over an arbitrary base…
We generalize Wagoner's representation of the automorphism group of a two-sided subshifts of finite type as the fundamental group of a certain CW-complex to groupoids having a certain refinement structure. This significantly streamlines the…