Extremal loop weight modules and tensor products for quantum toroidal algebras

We define integrable representations of quantum toroidal algebras of type A by tensor product, using the Drinfeld "coproduct". This allow us to recover the vector representations recently introduced by Feigin-Jimbo-Miwa-Mukhin [6] and constructed by the author [21] as a subfamily of extremal loop weight modules. In addition we get new extremal loop weight modules as subquotients of tensor powers of vector representations. As an application we obtain finite-dimensional representations of quantum toroidal algebras by specializing the quantum parameter at roots of unity.Comment: 30 page

Should there be more women in science and engineering?

Many people hold this truth to be self-evident, that there should be more female students in science and engineering. Typical arguments include possible benefits to women, possible benefits to the economy, and the unfairness of the current female under-representation. However, these justifications are never explicitly and thoroughly presented. Clearly stating and scrutinizing them, we show that they in fact have logical flaws. When made consistent, these arguments do not unconditionally justify enrolling more women in scientific disciplines. In particular, what women want must be taken into account. Outreach programs towards K-12 girls must therefore purport to allow them to choose a field freely, rather than try to draw as many of them to scientific disciplines as possible. This change of mindset must be accompanied by a close examination of the purpose and effects of these programs

Dissipation and nonlocality in a general expanding braneworld universe

We study the evolution of both scalar and tensor cosmological perturbations in a Randall-Sundrum braneworld having an arbitrary expansion history. We adopt a four dimensional point of view where the degrees of freedom on the brane constitute an open quantum system coupled to an environment composed of the bulk gravitons. Due to the expansion of the universe, the brane degrees of freedom and the bulk degrees of freedom interact as they propagate forward in time. Brane excitations may decay through the emission of bulk gravitons which may escape to future infinity, leading to a sort of dissipation from the four dimensional point of view of an observer on the brane. Bulk gravitons may also be reflected off of the curved bulk and reabsorbed by the brane, thereby transformed into quanta on the brane, leading to a sort of nonlocality from the four dimensional point of view. The dissipation and the nonlocality are encoded into the retarded bulk propagator. We estimate the dissipation rates of the bound state as well as of the matter degrees of freedom at different cosmological epochs and for different sources of matter on the brane. We use a near-brane limit of the bulk geometry for the study when purely nonlocal bulk effects are encountered.Comment: v2, 34 pages, 7 figures, minor changes, comments and references added, version to appear in Phys. Rev.