On commuting varieties of nilradicals of Borel subalgebras of reductive Lie algebras

Let $G$ be a connected reductive algebraic group defined over an algebraically closed field \mathbbm k of characteristic zero. We consider the commuting variety $\mathcal C(\mathfrak u)$ of the nilradical $\mathfrak u$ of the Lie algebra $\mathfrak b$ of a Borel subgroup $B$ of $G$. In case $B$ acts on $\mathfrak u$ with only a finite number of orbits, we verify that $\mathcal C(\mathfrak u)$ is equidimensional and that the irreducible components are in correspondence with the {\em distinguished} $B$-orbits in $\mathfrak u$. We observe that in general $\mathcal C(\mathfrak u)$ is not equidimensional, and determine the irreducible components of $\mathcal C(\mathfrak u)$ in the minimal cases where there are infinitely many $B$-orbits in $\mathfrak u$.Comment: 10 page

Costs of Control in Groups

This paper explores the role of social groups in explaining the reaction to control.We propose a simple model with a principal using control devices and a controlledagent, which incorporates the existence of social groups. Testing experimentally theconjectures derived from the model and related literature, we find that agents in socialgroups (i) perform more than other (no-group) agents; (ii) expect less control thanno-group agents; (iii) decrease their performance substantially when actual controlexceeds their expectation, while no-group agents do not react; (iv) do not reciprocatewhen facing less control than expected, while no-group agents do.

On Social Identity, Subjective Expectations, and the Costs of Control

Controlling employees can have severe consequences in situations that are not fully contractible. However, the perception of control may be contingent on the nature of the relationship between principal and agent. We, therefore, propose a principal-agent model of control that takes into account social identity (in the sense of Akerlof and Kranton, 2000, 2005). From the model and previous literature, we conclude that a shared social identity between the principal and agent has both a cognitive, that is, belief-related, and a behavioral, that is, performance-related, dimension. We test these theoretical conjectures in a labor market experiment with perfect monitoring. Our ndings confirm that social identity has important implications for the agent's decision-making. First, agents who are socially close to the principal (in-group) perform, on average, more on behalf of the principal than socially distant (no-group) agents. Second, social identity shapes the agent's subjective expectations of the acceptable level of control. In-group agents expect to experience less control than no-group agents. Third, an agent's reaction to the monitoring level she eventually faces also depends on social identity. If the experienced level of control is lower than the expected control level, that is, the agent faces a positive sensation, the increase in performance is less pronounced for in-group agents than for no-group agents. In the case of a negative sensation, however, in-group agents react stronger than no-group agents. Put differently, being socially distant from the principal amplies the performance-enhancing effect of a positive control surprise and mitigates the detrimental performance effect of a negative surprise.Control, Identity, Employee motivation, Principal-agent theory, Lab experiment

Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and seven

Let G(q) be a finite Chevalley group, where q is a power of a good prime p, and let U(q) be a Sylow p-subgroup of G(q). Then a generalized version of a conjecture of Higman asserts that the number k(U(q)) of conjugacy classes in U(q) is given by a polynomial in q with integer coefficients. In an earlier paper, the first and the third authors developed an algorithm to calculate the values of k(U(q)). By implementing it into a computer program using GAP, they were able to calculate k(U(q)) for G of rank at most 5, thereby proving that for these cases k(U(q)) is given by a polynomial in q. In this paper we present some refinements and improvements of the algorithm that allow us to calculate the values of k(U(q)) for finite Chevalley groups of rank six and seven, except E_7. We observe that k(U(q)) is a polynomial, so that the generalized Higman conjecture holds for these groups. Moreover, if we write k(U(q)) as a polynomial in q-1, then the coefficients are non-negative. Under the assumption that k(U(q)) is a polynomial in q-1, we also give an explicit formula for the coefficients of k(U(q)) of degrees zero, one and two.Comment: 16 page

Orbits of parabolic subgroups on metabelian ideals

We consider the action of a parabolic subgroup of the General Linear Group on a metabelian ideal. For those actions, we classify actions with finitely many orbits using methods from representation theory.Comment: 10 pages, 6 eps figure

The origin of IRS 16: dynamically driven inspiral of a dense star cluster to the Galactic center?

We use direct N-body simulations to study the inspiral and internal evolution of dense star clusters near the Galactic center. These clusters sink toward the center due to dynamical friction with the stellar background, and may go into core collapse before being disrupted by the Galactic tidal field. If a cluster reaches core collapse before disruption, its dense core, which has become rich in massive stars, survives to reach close to the Galactic center. When it eventually dissolves, the cluster deposits a disproportionate number of massive stars in the innermost parsec of the Galactic nucleus. Comparing the spatial distribution and kinematics of the massive stars with observations of IRS 16, a group of young He I stars near the Galactic center, we argue that this association may have formed in this way.Comment: 15 pages, Accepted for publiction in Ap