Classification of graded Hecke algebras for complex reflection groups

The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well as complex reflection groups. Received: July 25, 2001     

Discreteness Criterions of Isometric Subgroups for Quaternionic Hyperbolic Space

In this paper, we give analogue of Jörgensen's inequality for nonelementary groups of isometries of complex hyperbolic 2-space generated by two elements, one of which is either loxodromic or boundary elliptic for the same group of isometries of quaternionic hyperbolic 2-space. And we give a sufficient condition for a nonelementary subgroup of isometries of quaternionic hyperbolic 2-space generated by two elements one of which is parabolic not to be discrete.     

Topologically knotted Lagrangians in simply connected four-manifolds

Vidussi was the first to construct knotted Lagrangian tori in simply connected four-dimensional manifolds. Fintushel and Stern introduced a second way to detect such knotting. This note demonstrates that similar examples may be distinguished by the fundamental group of the exterior.

     

All Subvarieties of ℒpq Have Finite Bases of Identities

We consider the varieties of lattice ordered groups with the identity of commutation of the nth powers of elements. We establish that every such l-variety with n=pq, where p and q are distinct prime numbers, has a finite basis of identities.     

A Generalization of a Two-Parameter Quantization for the Group GL 2(k)

We generalize a well-known two-parameter quantization for the group GL ₂(k) (over an arbitrary field k). Specifically, a certain class of Hopf algebras is constructed containing that quantization. The algebras are constructed given an arbitrary coalgebra and an arbitrary pair of its commuting anti-isomorphisms, and are defined by quadratic relations. They are densely linked to the compact quantum groups introduced by Woronowicz. We give examples of Hopf algebras that can be rowed up to the two-parameter quantization for GL ₂(k).     

Weak Attractive Ligand–Polymer and Related Interactions in Catalysis and Reactivity: Impact,Applications, and Modeling

The notion of weak attractive ligand–polymer interactions is introduced, and its potential application, importance, and conceptual links with “cooperative” ligand–substrate interactions are discussed. Synthetic models of weak attractive ligand–polymer interactions are described, in which intramolecular weak C? H???F? C interactions (the existence of which remains contentious) have been detected by NMR spectroscopy and neutron and X‐ray diffraction experiments. These C? H???F? C interactions carry important implications for the design of catalysts for olefin polymerization, because they provide support for the practical feasibility of ortho‐F???H_β ligand–polymer contacts proposed for living Group 4 fluorinated phenoxyimine catalysts. The notion of weak attractive noncovalent interactions between an “active” ligand and the growing polymer chain is a novel concept in polyolefin catalysis.     

On Two Theorems of Finite Solvable Groups

For a finite group G, let T（G） denote a set of primes such that a prime p belongs to T（G） if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions： （1） G has a p-complement for each p∈T（G）; （2）│T（G）│= 2： （3） the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T（G）; then G either is solvable or G/Sol（G）≌PSL（2, 7） where Sol（G） is the largest solvable normal subgroup of G.     

Some New uniform frames with block size four and index one or three

In this paper, some new uniform frames with block size four and index one or three are obtained. The known existence results for (4,1)‐frames and (4,3)‐frames are both improved to the extent that only a finite number of possible exceptions remain. © 2003 Wiley Periodicals, Inc.     

Preparation of a cyclodextrin dimer linked with a bis(picolinyl)cystine moiety and its intra- and intermolecular inclusion behavior

A novel cyclodextrin (CD) dimer linked with a bis(picolinyl)cystine (Cys) moiety was prepared by the coupling of Boc-protected Cys with amino-modified CDs, followed by deprotection of the Boc groups and bispicolinylation. The dimer showed less affinity to an organic guest molecule compared to that of a native CD monomer. It was attributed to an intramolecular inclusion of the pyridine moiety into CD cavity. The dimer caused significant increase of its organic guest affinity by an addition of a copper ion. The included pyridine group may come out of a CD cavity to bind the copper ion and the two CDs included cooperatively and intermolecularly a guest molecule with high affinity.     

Thermolyzable polymer networks and star polymers containing a novel,compact, degradable acylal‐based dimethacrylate cross‐linker: Synthesis,characterization, and thermolysis

A compact, cleavable acylal dimethacrylate cross‐linker, 1,1‐ethylenediol dimethacrylate (EDDMA), was synthesized from the anhydrous iron(III) chloride‐catalyzed reaction between methacrylic anhydride and acetaldehyde. The ability of EDDMA to act as cross‐linker was demonstrated by using it for the preparation of one neat cross‐linker network, four star polymers of methyl methacrylate (MMA), and four randomly cross‐linked MMA polymer networks using group transfer polymerization (GTP). For comparison, the corresponding polymer structures based on the commercially available ethylene glycol dimethacrylate (EGDMA) cross‐linker (isomer of EDDMA) were also prepared via GTP. The number of arms of the EDDMA‐based star polymers was lower than that of the corresponding EGDMA polymers, whereas the degrees of swelling in tetrahydrofuran of the EDDMA‐based MMA networks were higher than those of their EGDMA‐based counterparts. Although none of the EDDMA‐containing polymers could be cleanly hydrolyzed under basic or acidic conditions, they could be thermolyzed at 200 °C within 1 day giving lower molecular weight products. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5811–5823, 2007