Induced conjugacy classes and induced U_e(G)-modules

By work of De Concini, Kac and Procesi the irreducible representations of the non-restricted specialization of the quantized enveloping algebra of the Lie algebra g at the roots of unity are parametrized by the conjugacy classes of a group G with Lie(G)=g. We show that there is a natural dimension preserving bijection between the sets of irreducible representations associated with conjugacy classes lying in the same Jordan class (decomposition class). We conjecture a relation for representations associated with classes lying in the same sheet of G, providing two alternative formulations. We underline some evidence and illustrate potential consequences.Comment: This paper is an expanded version of a lecture given at the conference "Hopf algebras and tensor categories", Almeri'a, July 2011. It will appear in the volume of Contemporary Math. containing the conference Proceeding

Sub-and near-barrier fusion reactions experimental results

Early data of sub-barrier fusion teached us that cross sections may strongly depend on the structure of colliding nuclei and on couplings to transfer channels. The influence of transfer is clearly indicated in the excitation functions of different nickel isotopes and various Ca+Zr systems. Fusion barrier distributions often yield the fingerprint of the relevant inelastic and transfer couplings. At lower energies, far below the barrier the slope of the excitation function keeps increasing in many cases, so that the cross sections are strongly over-predicted by standard coupled-channels (CC) calculations; this was named a hindrance effect. Furthermore, light heavy-ion systems show cross section oscillations above the Coulomb barrier. Recent experiments have been performed on the fusion of 28,30Si+28,30Si systems where all phenomena cited above show up. In particular regular oscillations that have been revealed above the barrier for 28Si+28Si and have been interpreted as the consequence of the strong channel couplings and/or the oblate deformation of 28Si

Arab-Islamic reception of Hellenistic science

This article is an overview of the Arab-Islamic reception and development of Hellenistic science. It particularly refers to mathematics, physics and astronomy. It focuses on the following topics: 1) Two interpretative models of this reception in the 19th, 20th, and 21st century scholarship: the “Indo-European model” (which supposes a cultural heterogeneity between Greece and Islam) and the “cosmopolitan Hellenistic model” (which supposes homogeneity between the two). 2) The channels through which Hellenistic science was transmitted to the Islamic world: the philological channel, and the oral channel which implies the pre-existence of a common Greek-Semitic cultural ground that made this transmission possible. 3) Three features of the Arab-Islamic sciences that highlight their essential contribution to the emergence of modern science in 16th and 17th century Europe: 3.1. The “democratising” character of the Arab-Islamic sciences resulting from a larger diffusion of literacy. 3.2. The higher precision of measurements and calculations. 3.3. The experimental approach of Muslim scientists. A positive role in the accomplishment of these advances has been played by the non-metaphysical character of orthodox Islamic monotheism. According to Muslim orthodoxy, there are no Neo-Platonic intermediaries between the almighty God and his creation. The whole universe is submitted to the same physical laws. I argue that today it is important to open an interdisciplinary debate on the Arab-Islamic sciences. It would certainly lead to a better appreciation of their historical contribution. It could also suggest answers to contemporary epistemological impasses deriving from the growing gap between the humanities and the sciences.status: publishe

Spherical conjugacy classes and Bruhat decomposition

Let G be a connected, reductive algebraic group over an algebraically closed field of characteristic zero or good and odd. We characterize the spherical conjugacy classes of G as those intersecting only Bruhat cells corresponding to involutions in the Weyl group of G.Comment: Final version, to appear in Ann. Inst. Fourier, Grenobl