Poisson homology of r-matrix type orbits I: example of computation

In this paper we consider the Poisson algebraic structure associated with a classical $r$-matrix, i.e. with a solution of the modified classical Yang--Baxter equation. In Section 1 we recall the concept and basic facts of the $r$-matrix type Poisson orbits. Then we describe the $r$-matrix Poisson pencil (i.e the pair of compatible Poisson structures) of rank 1 or $CP^n$-type orbits of $SL(n,C)$. Here we calculate symplectic leaves and the integrable foliation associated with the pencil. We also describe the algebra of functions on $CP^n$-type orbits. In Section 2 we calculate the Poisson homology of Drinfeld--Sklyanin Poisson brackets which belong to the $r$-matrix Poisson family

Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the associated standard constructions. This extends a characterization of equivariant de Rham cohomology in terms of derived functors developed earlier for the special case where the Lie groupoid is an ordinary Lie group, viewed as a Lie groupoid with a single object; in that theory over a Lie group, the ordinary Bott-Dupont-Shulman-Stasheff complex arises as an a posteriori object. We prove that, given a locally trivial Lie groupoid G and a smooth G-manifold f over the space B of objects of G, the resulting G-equivariant de Rham theory of f boils down to the ordinary equivariant de Rham theory of a vertex manifold relative to the corresponding vertex group, for any vertex in the space B of objects of G; this implies that the equivariant de Rham cohomology introduced here coincides with the stack de Rham cohomology of the associated transformation groupoid whence this stack de Rham cohomology can be characterized as a relative derived functor. We introduce a notion of cone on a Lie-Rinehart algebra and in particular that of cone on a Lie algebroid. This cone is an indispensable tool for the description of the requisite monads.Comment: 47 page

Irreducible Characters of General Linear Superalgebra and Super Duality

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical Kazhdan-Lusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category \mc{O} of the general linear superalgebra. We also prove the super duality conjecture

The rhetoric of the consumer and customer control in China

This article explores the extent to which the rhetoric of the sovereign consumer and the use of the customer as a device of managerial control have been transferred to the subsidiaries of multinational retail firms operating in China. Based upon data drawn from over 200 interviews conducted at UK and Japanese multi-nationals' stores, in this rapidly internationalizing context it was evident that the notion of the sovereign consumer was ubiquitous and procedures designed to inculcate management by customers or consumer control had been implemented. However, it was equally apparent that the rhetoric of the consumer not only served managerial ends, but also provided a rich and fertile resource for shopfloor workers. Meaningful, socially embedded relationships could also play a crucial role in transactions. Moreover, with respect to discipline and control, employees were fully aware that power lay with their managers, rather than disembodied consumers or even actual customers

Customer emotions in service failure and recovery encounters

Emotions play a significant role in the workplace, and considerable attention has been given to the study of employee emotions. Customers also play a central function in organizations, but much less is known about customer emotions. This chapter reviews the growing literature on customer emotions in employee–customer interfaces with a focus on service failure and recovery encounters, where emotions are heightened. It highlights emerging themes and key findings, addresses the measurement, modeling, and management of customer emotions, and identifies future research streams. Attention is given to emotional contagion, relationships between affective and cognitive processes, customer anger, customer rage, and individual differences

Work-life, diversity and intersectionality: a critical review and research agenda

Work-life issues have important implications at both organizational and individual levels. This paper provides a critical review of the work-life literature from 1990 onwards through the lens of diversity, with a particular focus on disparities of power induced by methodological and conceptual framings of work and life. The review seeks to answer the following questions: What are the gaps and omissions in the work-life research? How may they be overcome? To answer these questions, the review scrutinizes blind spots in the treatment of life, diversity and power in work-life research in both positivist and critical scholarship. In order to transcend the blind spots in positivist and critical work-life research, the review argues the case for an intersectional approach which captures the changing realities of family and workforce through the lens of diversity and intersectionality. The theoretical contribution is threefold: first, the review demonstrates that contemporary framing of life in the work-life literature should be expanded to cover aspects of life beyond domestic life. Second, the review explains why and how other strands of diversity than gender also manifest as salient causes of difference in experiences of the work-life interface. Third, the review reveals that social and historical context has more explanatory power in work-life dynamics than the micro-individual level of explanations. Work-life literature should capture the dynamism in these contexts. The paper also provides a set of useful recommendations to capture and operationalize methodological and theoretical changes required in the work-life literature