相关论文: Finite dimensional vertex
In this manuscript, we give a classification of all irreducible, unitary representations of complex spin groups.
In this note the smooth (i.e. with open stabilizers) linear and {\sl semilinear} representations of certain permutation groups (such as infinite symmetric group or automorphism group of an infinite-dimensional vector space over a finite…
Within the context of the extended bi-spinor gauge theory we describe a new off-shell realization of scalar supersymmetry (s-susy) of massless interacting fields with U(1), U(1) x SU(N) and U(1) x SU(N_1) x SU(N_2) gauge groups. S-susy acts…
We construct an irreducible representation for the extended affine algebra of type $sl_2$ with coordinates in a quantum torus. We explicitly give formulas using vertex operators similar to those found in the theory of the infinite rank…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
We study the minimal unitary representation (minrep) of SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2) describes a massless conformal scalar…
We consider a category whose morphisms are bordisms of $n$-dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product $G$ of $(n+1)$ copies of infinite symmetric group. We…
We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.
In this paper we present a complete classification (isomorphism classes with some isomorphism invariants) of complex associative algebras up to dimension five (including both cases: unitary and non-unitary). In some symbolic computations we…
We construct integrated and unintegrated vertex operators for the type II superstring using the B-RNS-GSS formalism. The construction is done in flat spacetime background for both type II superstrings and type IIB superstring in a…
Positive energy unitary irreducible representations of $SU(2,2)$ can be constructed with the aid of bosonic oscillators in (anti)fundamental representation of $SU(2)_L\times SU(2)_R$ that are closely related to Penrose twistors. Starting…
In this note we construct mixed dimensional infinite soliton trains, which are solutions of nonlinear Schr\"odinger equations whose asymptotic profiles at time infinity consist of infinitely many solitons of multiple dimensions. For example…
We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…
Infinite enlargements of finite pseudo-unitary symmetries are explicitly provided in this letter. The particular case of u(2,2)=so(4,2)+u(1) constitutes a (Virasoro-like) infinite-dimensional generalization of the 3+1-dimensional conformal…
A new procedure was recently proposed for constructing massless Type IIB vertex operators in the pure spinor formalism. Instead of expressing these closed string vertex operators as left-right products of open string vertex operators, they…
The aim of this paper is to apply systematically to AdS_4 some modern tools in the representation theory of Lie algebras which are easily generalised to the supersymmetric and quantum group settings and necessary for applications to string…
We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…
Fock module realization for the unitary singleton representations of the $d-1$ dimensional conformal algebra $o(d-1,2)$, which correspond to the spaces of one-particle states of massless scalar and spinor in $d-1$ dimensions, is given. The…
We present the dictionary between the one-particle Hilbert spaces of totally symmetric tensor-spinor fields of spin $s={3}/{2}, {5}/{2}$ with any mass parameter on $D$-dimensional ($D \geq 3$) de Sitter space ($dS_{D}$) and Unitary…
The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the $\overline{SL(2,R)}$ group. In the case of $(2j+1)$-dimensional…