相关论文: Finite dimensional vertex

We show that each unitary representation of the N=2 superVirasoro algebra can be realized in terms of ``collective excitations'' over a filled Dirac sea of fermionic operators satisfying a generalized exclusion principle. These are…

A physical and geometrical interpretation of previously introduced tensor operator algebras of U(2,2) in terms of algebras of higher-conformal-spin quantum fields on the anti-de Sitter space AdS_5 is provided. These are higher-dimensional…

We show that the Lax pair of the pure spinor superstring in AdS5xS5 admits a generalization where the generators of the superconformal algebra are replaced by the generators of some infinite-dimensional Lie superalgebra.

The method of nonlinear realizations is applied for the conformally invariant description of the spinning particles in terms of geometrical quantities of the parameter spaces of the one dimensional N - extended superconformal groups. We…

For countably infinite IFSs on $\mathbb R^2$ consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound for the Hausdorff dimension and a lower bound for the lower…

The purpose of this paper is to investigate the global categorical symmetries that arise when gauging finite higher groups in three or more dimensions. The motivation is to provide a common perspective on constructions of non-invertible…

We formulate gauge invariant interactions of totally symmetric tensor and tensor-spinor higher spin gauge fields in AdS(5) that properly account for higher-spin-gravitational interactions at the action level in the first nontrivial order.

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

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…

We derive an explicit expression for an associative *-product on fuzzy complex projective spaces. This generalises previous results for the fuzzy 2-sphere and gives a discrete non-commutative algebra of functions on fuzzy complex projective…

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete…

We introduce the notions of symmetric and symmetrizable representations of $\text{SL}_2(\mathbb{Z})$. The linear representations of $\text{SL}_2(\mathbb{Z})$ arising from modular tensor categories are symmetric and have congruence kernel.…

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

This is a comprehensive review of the worldsheet techniques for the quantization of type IIB superstring theory on the AdS_5 x S^5 background, using the pure spinor formalism. Particular emphasis is devoted to AdS/CFT applications, with…

We classify representations of the mapping class group of a surface of genus $g$ (with at most one puncture or boundary component) up to dimension $3g-3$. Any such representation is the direct sum of a representation in dimension $2g$ or…

This review gives results on vertex operators for the Type IIB superstring in an AdS3 x S3 background with Ramond-Ramond flux, which were presented at Strings 2000. Constraint equations for these vertex operators are derived, and their…

We prove that every closed orientable surface S of negative Euler characteristic admits a pair of finite-degree covers which are length isospectral over S but generically not simple length isospectral over S. To do this, we first…

Using the pure spinor formalism, a quantizable sigma model has been constructed for the superstring in an AdS_5 x S^5 background with manifest PSU(2,2|4) invariance. The PSU(2,2|4) metric g_{AB} has both vector components g_{ab} and spinor…

This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras…

We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.