相关论文: A proof of the continuous Dyson-Maleev representat…
The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher…
Let $\Gamma$ be a lattice in a connected semisimple Lie group $G$ with trivial center and no compact factors. We introduce a volume invariant for representations of $\Gamma$ into $G$, which generalizes the volume invariant for…
Supersymmetric field theories on noncommutative spaces are constructed. We present two different representations of noncommutative space, but we can obtain supersymmetry algebla and supersymmetric Yang-Mills action independent of its…
Induced supersymmetry representations on composite operators are studied. In superspace the ensuing transformation rules (trivially) lead to an effective superfield. On the other hand, an induced representation must exist for non-linear…
We study the extraordinary dimension function dim_{L} introduced by \v{S}\v{c}epin. An axiomatic characterization of this dimension function is obtained. We also introduce inductive dimensions ind_{L} and Ind_{L} and prove that for…
The derivation of the boson representation of spin operators is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the corresponding cases. The suggested formalism allows to address some subtle issues which…
This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic…
We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group $S_\infty$, the automorphism group of the countable dense linear order, the…
Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Gamma be the fundamental group of a compact orientable surface of genus at least 2. We survey the study of maximal representations,…
We revisit the higher spin extensions of the anti de Sitter algebra in four dimensions that incorporate internal symmetries and admit representations that contain fermions, classified long ago by Konstein and Vasiliev. We construct the…
We present a definition of indefinite Kasparov modules, a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. Our main theorem shows that to each indefinite Kasparov module we…
The Drinfeld-Sokolov construction of integrable hierarchies, as well as its generalizations, may be extended to the case of loop superalgebras. A sufficient condition on the algebraic data for the resulting hierarchy to be invariant under…
The recent developments towards the possible non-perturbative formulation of string/M theory using supersymmetric Yang-Mills matrix models (SYMs) are discussed. In the first part, we give a critical review on the status of our present…
We settle a long standing issue concerning the traditional derivation of non-compact non-linear sigma models in the theory of disordered electron systems: the hyperbolic Hubbard-Stratonovich (HS) transformation of Pruisken-Schaefer type.…
The Representation Theorem by Zomorodian and Carlsson has been the starting point of the study of persistent homology under the lens of algebraic representation theory. In this work, we give a more accurate statement of the original theorem…
We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We…
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…
Smooth pseudodifferential operators on $\mathbb{R}^n$ can be characterized by their mapping properties between $L^p-$Sobolev spaces due to Beals and Ueberberg. In applications such a characterization would also be useful in the non-smooth…
We establish an invariance principle corresponding to the universality of random matrices. More precisely, we prove the dynamical universality of random matrices in the sense that, if the random point fields $ \muN $ of $ \nN $-particle…
Vershik and Kerov gave asymptotical bounds for the maximal and the typical dimensions of irreducible representations of symmetric groups $S_n$. It was conjectured by G. Olshanski that the maximal and the typical dimensions of the isotypic…