Do you want to publish a course? Click here

Study-type determinants and their properties

49   0   0.0 ( 0 )
 Added by Naoya Yamaguchi
 Publication date 2018
  fields
and research's language is English




Ask ChatGPT about the research

In this paper, we define the concept of the Study-type determinant, and we present some properties of these determinants. These properties lead to some properties of the Study determinant. The properties of the Study-type determinants are obtained using a commutative diagram. This diagram leads not only to these properties, but also to an inequality for the degrees of representations and to an extension of Dedekinds theorem.

rate research

Read More

In this paper we study properties of a homomorphism $rho$ from the universal enveloping algebra $U=U(mathfrak{gl}(n+1))$ to a tensor product of an algebra $mathcal D(n)$ of differential operators and $U(mathfrak{gl}(n))$. We find a formula for the image of the Capelli determinant of $mathfrak{gl}(n+1)$ under $rho$, and, in particular, of the images under $rho$ of the Gelfand generators of the center $Z(mathfrak{gl}(n+1))$ of $U$. This formula is proven by relating $rho$ to the corresponding Harish-Chandra isomorphisms, and, alternatively, by using a purely computational approach. Furthermore, we define a homomorphism from $mathcal D(n) otimes U(mathfrak{gl}(n))$ to an algebra containing $U$ as a subalgebra, so that $sigma (rho (u)) - u in G_1 U$, for all $u in U$, where $G_1 = sum_{i=0}^{n} E_{ii}$.
The largest eigenvalue of a networks adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically grounded expression relating the value of the largest eigenvalue of a given network to the largest eigenvalue of two network subgraphs, considered as isolated: The hub with its immediate neighbors and the densely connected set of nodes with maximum $K$-core index. We validate this formula showing that it predicts with good accuracy the largest eigenvalue of a large set of synthetic and real-world topologies. We also present evidence of the consequences of these findings for broad classes of dynamics taking place on the networks. As a byproduct, we reveal that the spectral properties of heterogeneous networks built according to the linear preferential attachment model are qualitatively different from those of their static counterparts.
We introduce a generalization of the notion of a negligible morphism and study the associated tensor ideals and thick ideals. These ideals are defined by considering deformations of a given monoidal category $mathcal{C}$ over a local ring $R$. If the maximal ideal of $R$ is generated by a single element, we show that any thick ideal of $mathcal{C}$ admits an explicitely given modified trace function. As examples we consider various Deligne categories and the categories of tilting modules for a quantum group at a root of unity and for a semisimple, simply connected algebraic group in prime characteristic. We prove an elementary geometric description of the thick ideals in quantum type A and propose a similar one in the modular case.
We investigate the fundamental properties of quantum Borcherds-Bozec algebras and their representations. Among others, we prove that the quantum Borcherds-Bozec algebras have a triangular decomposition and the category of integrable representations is semi-simple.
Let $Gamma$ be a generic subgroup of the multiplicative group $mathbb{C}^*$ of nonzero complex numbers. We define a class of Lie algebras associated to $Gamma$, called twisted $Gamma$-Lie algebras, which is a natural generalization of the twisted affine Lie algebras. Starting from an arbitrary even sublattice $Q$ of $mathbb Z^N$ and an arbitrary finite order isometry of $mathbb Z^N$ preserving $Q$, we construct a family of twisted $Gamma$-vertex operators acting on generalized Fock spaces which afford irreducible representations for certain twisted $Gamma$-Lie algebras. As application, this recovers a number of known vertex operator realizations for infinite dimensional Lie algebras, such as twisted affine Lie algebras, extended affine Lie algebras of type $A$, trigonometric Lie algebras of series $A$ and $B$, unitary Lie algebras, and $BC$-graded Lie algebras.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا