Quantized Flag Manifolds and Irreducible *-Representations

In this paper we fill some gaps in the arguments of our previous papers [1,2]. In particular, we give a proof that the L operators of Conformal Field Theory indeed satisfy the defining relations of the Yang–Baxter algebra. Among other results we present a derivation of the functional relations satisfied by T and Q operators and a proof of the basic analyticity assumptions for these operators used in [1,2]. Received: 20 May 1998 / Accepted: 7 July 1998     

The emergence of groups in the evolution of friendship networks

Friendship networks usually show a certain degree of segmentation: subgroups of friends. The explanation of the emergence of such groups from initially dyadic pair friendships is a difficult but important problem. In this paper we attempt to provide a first contribution to the explanation of subgroup formation in friendship networks by using the LS set as a definition for a friendship group. We construct a dynamic individual oriented model of friendship formation and provide preliminary simulation results that give an idea of how to continue the process of explaining group formation.     

Evolution of sociology freshmen into a friendship network

In this paper we both describe and analyze the meeting process and the evolution of a friendship network among sociology freshmen in the Netherlands. We develop a theory that explains how changes in the network structure depend on one or more of four main effects: proximity, visible similarity, invisible similarity, and network opportunity. We formulate expectations with regard to what factors are important at what stages of the friendship development, making a distinction between 'meeting' and 'mating.' To some extent, the results confirm our expectations. The proximity and visible similarity variables determine change in network structure in the early stages, whereas network opportunity is important during all stages. Unfortunately, no significant effects of invisible similarity are found.     

Vertex-IRF transformations, dynamical quantum groups and harmonic analysis

It is shown that a dynamical quantum group arising from a vertex-IRF transformation has a second realization with untwisted dynamical multiplication but nontrivial bigrading. Applied to the SL 2; ) dynamical quantum group, the second realization is naturally described in terms of Koornwinder's twisted primitive elements. This leads to an intrinsic explanation why harmonic analysis on the “classical” SL(2; ) quantum group with respect to twisted primitive elements, as initiated by Koornwinder, is the same as harmonic analysis on the SL(2; C) dynamical quantum group.     

Reflection equation algebras, coideal subalgebras, and their centres

Reflection equation algebras and related U_q(\mathfrak g){U{_q}(\mathfrak g)} -comodule algebras appear in various constructions of quantum homogeneous spaces and can be obtained via transmutation or equivalently via twisting by a cocycle. In this paper we investigate algebraic and representation theoretic properties of such so called ‘covariantized’ algebras, in particular concerning their centres, invariants, and characters. The locally finite part F_l(U_q (\mathfrak g)){F_l(U{_q} (\mathfrak g))} of U_q(\mathfrak g){U{_q}(\mathfrak g)} with respect to the left adjoint action is a special example of a covariantized algebra. Generalising Noumi’s construction of quantum symmetric pairs we define a coideal subalgebra B _f of U_q(\mathfrak g){U{_q}(\mathfrak g)} for each character f of a covariantized algebra. We show that for any character f of F_l(U_q(\mathfrak g)){F_l(U{_q}(\mathfrak g))} the centre Z(B _f ) canonically contains the representation ring Rep(\mathfrak g){{\rm Rep}(\mathfrak g)} of the semisimple Lie algebra \mathfrak g{\mathfrak g} . We show moreover that for \mathfrak g = \mathfrak sl_n(\mathbb C){\mathfrak g = {\mathfrak sl}_n(\mathbb C)} such characters can be constructed from any invertible solution of the reflection equation and hence we obtain many new explicit realisations of Rep(\mathfrak sl_n(\mathbb C)){{\rm Rep}({\mathfrak sl}_n(\mathbb C))} inside U_q(\mathfrak sl_n(\mathbb C)){U_q({\mathfrak sl}_n(\mathbb C))} . As an example we discuss the solutions of the reflection equation corresponding to the Grassmannian manifold Gr(m,2m) of m-dimensional subspaces in \mathbb C^2m{{\mathbb C}^{2m}}.     

Multivariable BC Type Askey-Wilson Polynomials With Partly Discrete Orthogonality Measure

The multivariable BC type Askey-Wilson polynomials are considered for a parameter domain such that the orthogonality measure has partly discrete and partly continuous support.     

Object oriented modeling of social networks

The aim of this paper is to explain principles of object oriented modeling in the scope of modeling dynamic social networks. As such, the approach of object oriented modeling is advocated within the field of organizational research that focuses on networks.We provide a brief introduction into the field of social networks and present an overview of existing network models and methods. Subsequently we introduce an elementary problem field in the social sciences in general, and in studies of organizational change and design in particular: the micro-macro link. We argue that the most appropriate way to hadle this problem is the principle of methodological individualism. For social network analysis, to contribute to this theoretical perspective, it should include an individual choice mechanism and become more dynamically oriented. Subsequently, object oriented modeling is advocated as a tool to meet these requirements for social network analysis. We show that characteristics of social systems that are emphasized in the methodological individualistic approach have their direct equivalences in object oriented models. The link between the micro level where actors act, and the macro level where phenomena occur as a consequence and cause of these actions, can be modelled in a straightforward way.     

Is politics power or policy oriented? A comparative analysis of dynamic access models in policy networks*

We will show that these base models and some intermediate ones result in fundamentally different network structures and predicted outcomes. Moreover, we will show that the policy driven models do fundamentally better than the power driven models.

In policy networks actors use access relations to influence preferences of other actors. Establishment and shifts of access relations and their consequences for outcomes of decisions are the main focal points in this paper. Unlike most policy network studies, we therefore do not take the network and its relations as given and constant. Instead we device computer simulation models to account for the dynamics in policy networks. We compare different models and investigate the resulting network structures and predicted outcomes of decisions. The choice among the alternative models is made by their correspondence with empirical network structures and actual outcomes of decisions.

In our models, we assume that all relevant actors aim at policy outcomes as close as possible to their own preferences. Policy outcomes are determined by the preferences of the final decision makers at the moment of the vote. In general, only a small fraction of the actors takes part in the final vote. Most actors have therefore to rely on access relations for directly or indirectly shaping the preferences of the final decision makers. For this purpose actors make access requests to other actors. An access relation is assumed to be established if such a request is accepted by the other actor.

Access relations require time and resources. Actors are therefore assumed to be restricted in the number of access requests they can make and the number of requests they can accept Moreover, due to incomplete information and simultaneous actions by other actors, actors have to make simplifying assumptions in the selection of their “best” requests and learn by experience.

We device two base models that correspond to two basic views on the nature of political processes. In the first view politics is seen as power driven. Corresponding to this view, actors aim at access relations with the most powerful actors in the field. They estimate their likelihood of success by comparing their own resources with those of the target actors. Power also determines the order in which actors accept requests. In the second view, policy matters and actors roughly estimate the effects access relations might have on the outcome of decisions. Actors select requests to “bolster” their own preference as much as possible.