Inductive algebras and homogeneous shifts

Inductive algebras for the irreducible unitary representations of the universal cover of the group of unimodular two by two matrices are classified. The classification of homogeneous shift operators is obtained as a direct consequence. This gives a new approach to the results of Bagchi and Misra

Weighted Bergman kernels and virtual Bergman kernels

We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.Comment: 12 pages. One-hour lecture for graduate students, SCV 2004, August 2004, Beijing, P.R. China. V2: typo correcte

Catalytic Depolymerization of Lignin and Woody Biomass in Supercritical Ethanol:Influence of Reaction Temperature and Feedstock

The one-step ethanolysis approach to upgrade lignin to monomeric aromatics using a CuMgAl mixed oxide catalyst is studied in detail. The influence of reaction temperature (200-420 °C) on the product distribution is investigated. At low temperature (200-250 °C), recondensation is dominant, while char-forming reactions become significant at high reaction temperature (&gt;380 °C). At preferred intermediate temperatures (300-340 °C), char-forming reactions are effectively suppressed by alkylation and Guerbet and esterification reactions. This shifts the reaction toward depolymerization, explaining high monomeric aromatics yield. Carbon-14 dating analysis of the lignin residue revealed that a substantial amount of the carbon in the lignin residue originates from reactions of lignin with ethanol. Recycling tests show that the activity of the regenerated catalyst was strongly decreased due to a loss of basic sites due to hydrolysis of the MgO function and a loss of surface area due to spinel oxide formation of the Cu and Al components. The utility of this one-step approach for upgrading woody biomass was also demonstrated. An important observation is that conversion of the native lignin contained in the lignocellulosic matrix is much easier than the conversion of technical lignin.</p

Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3: corrected count of connected components for G=SU(p,q) (p \neq q); added due credits to the work of Xia and Markman-Xia; minor corrections and clarifications. 31 page