Regions of linearity, Lusztig cones and canonical basis elements for the quantized enveloping algebra of type A_4

Let U_q be the quantum group associated to a Lie algebra g of rank n. The negative part U^- of U has a canonical basis B with favourable properties, introduced by Kashiwara and Lusztig. The approaches of Kashiwara and Lusztig lead to a set of alternative parametrizations of the canonical basis, one for each reduced expression for the longest word in the Weyl group of g. We show that if g is of type A_4 there are close relationships between the Lusztig cones, canonical basis elements and the regions of linearity of reparametrization functions arising from the above parametrizations. A graph can be defined on the set of simplicial regions of linearity with respect to adjacency, and we further show that this graph is isomorphic to the graph with vertices given by the reduced expressions of the longest word of the Weyl group modulo commutation and edges given by long braid relations. Keywords: Quantum group, Lie algebra, Canonical basis, Tight monomials, Weyl group, Piecewise-linear functions.Comment: 61 pages, 17 figures, uses picte

Oh, Ye of Little (Good) Faith: Questions, Concerns and Commentary on Efforts to Regulate Participant Conduct in Mediations

There are many types of mediation. This article focuses exclusively on mediations within Professor Lande\u27s liti-mediation culture - those dealing with disputes that are or may become the subject of litigation. I address both court-connected and private mediations as I believe that the potential for bad faith exists in both. Following this Introduction, in Part II, I examine definitions of good faith in mediation, I then review commentary and case law on good faith requirements. In Part III, I argue that certain objectively determinable behavior ought to be proscribed. By contrast, some good faith standards adopted by courts or advocated by scholars, in my view, infringe upon parties\u27 rights of self-determination. These include requirements that parties make specific offers or that representatives possess adequate settlement authority. Part IV contains my suggestions for standards of good faith in mediation and discussion of how such standards might be implemented. My conclusions are set forth in Part V

Australian Books and Authors in the American Marketplace 1840s-1940s

Australian Books and Authors in the American Marketplace 1840s—1940s explores how Australian writers and their works were present in the United States before the mid twentieth century to a much greater degree than previously acknowledged. Drawing on fresh archival research and combining the approaches of literary criticism, print culture studies and book history, David Carter and Roger Osborne demonstrate that Australian writing was transnational long before the contemporary period. In mapping Australian literature’s connections to British and US markets, their research challenges established understandings of national, imperial and world literatures. Carter and Osborne examine how Australian authors, editors and publishers engaged productively with their American counterparts, and how American readers and reviewers responded to Australian works. They consider the role played by British publishers and agents in taking Australian writing to America, and how the international circulation of new literary genres created new opportunities for novelists to move between markets. Some of these writers, such as Christina Stead and Patrick White, remain household names; others who once enjoyed international fame, such as Dale Collins and Alice Grant Rosman, have been largely forgotten. The story of their books in America reveals how culture, commerce and copyright law interacted to create both opportunities and obstacles for Australian writers