Root Systems and Length Functions

We introduce root systems for those imprimitive complex reflection groups which are generated by involutory reflections, and study the associated length functions. These have many properties in common with the usual length functions for finite Weyl groups.     

Synthesis of deoxy sugar esters: a chemoenzymatic stereoselective approach affording deoxy sugar derivatives also in the form of aldehyde

A chemoenzymatic synthesis of deoxy sugar esters is described. The synthesis is based on the O-alkylation of carboxylic acid with 2-bromo-5-acetoxypentanal. The method allows treatment of hydroxy carboxylic acids without protection of alcoholic hydroxyl groups. Several stereoisomeric deoxy sugar esters were resolved (up to ee or de > 98%) using a lipase-catalyzed acetylation of hemiacetals that in certain cases afforded deoxy sugar derivatives in the form of aldehydes. The stereochemistry of the reactions was determined by the NMR spectra of mandelic acid derivatives.     

Regioselective intramolecular ring closure of 2-amino-6-bromo-2,6-dideoxyhexono-1,4-lactones to 5- or 6-membered iminuronic acid analogues: synthesis of 1-deoxymannojirimycin and 2,5-dideoxy-2,5-imino-D-glucitol

1-Deoxymannojirimycin (8c) was synthesised from 2-amino-6-bromo-2,6-dideoxy-D-mannono-1,4-lactone (7) by intramolecular direct displacement of the C-6 bromine employing non-aqueous base treatment followed by reduction of the intermediate methyl ester. Likewise, using aqueous base at pH 12, ring closure took place by 5-exo attack on the 5,6-epoxide leading to 2,5-dideoxy-2,5-imino-L-gulonic acid (9b), which was reduced to 2,5-dideoxy-2,5-imino-D-glucitol (9b). The method was further applied to 2-amino-6-bromo-2,6-dideoxy-D-galacto- as well as D-talo-1,4-lactones (14 and 15). However, only the corresponding six-membered ring 1,5-iminuronic acid mimetics, namely (2R,3R,4S,5R)-3,4,5-trihydroxypipecolic acid (2,6-dideoxy-2,6-imino-D-galactonic acid, 16) and (2S,3R,4S,5R)-3,4,5-trihydroxypipecolic acid (2,6-dideoxy-2,6-imino-D-talonic acid, 17), were obtained. The corresponding enantiomers, L-galacto- as well as L-talo-2-amino-6-bromo-2,6-dideoxy-1,4-lactones ent-14 and ent-15, reacted accordingly to give the D-galacto- and L-altro-1,5-iminuronic acid mimetics, (2S,3S,4R,5S)-3,4,5-trihydroxypipecolic acid (2,6-dideoxy-2,6-imino-L-galactonic acid, ent-16) and (2R,3S,4R,5S)-3,4,5-trihydroxypipecolic acids (2,6-dideoxy-2,6-imino-L-talonic acid, ent-17), respectively.     

Determination of captopril in human blood by gas chromatography-negative-ion chemical ionization mass spectrometry with [18O4]captopril as internal standard

A method for the quantitative measurement of captopril in human blood is described. Blood was immediately treated with N-ethylmaleimide to prevent oxidative degradation. The carboxyl moiety was derivatized to the pentafluorobenzyl ester, which shows excellent properties for negative-ion chemical ionization mass spectrometry. A stable isotope-labelled standard was prepared from the intact target molecule in quantitative yield by exchanging the oxygen atoms of the free carboxylic acid and the imide moiety against 18O. The detection limit under negative-ion chemical ionization conditions is ca. 100 times lower than under electron-impact or positive-ion chemical ionization conditions, therefore only very small amounts of the original sample have to be analysed. The method was applied to be quantitative determination of unchanged captopril in human plasma after oral administration of a 25-mg dose.     

Separating Characters by Blocks

We investigate the problem of finding a set of prime divisorsof the order of a finite group, such that no two irreduciblecharacters are in the same p-block for all primes p in the set.Our main focus is on the simple and quasi-simple groups. Forresults on the alternating and symmetric groups and their doublecovers, some combinatorial results on the cores of partitionsare proved, which may be of independent interest. We also studythe problem for groups of Lie type. The sporadic groups (andtheir relatives) are checked using GAP.     

Projective modules in the intersection cohomology of Deligne–Lusztig varieties

We formulate a strong positivity conjecture on characters afforded by the Alvis–Curtis dual of the intersection cohomology of Deligne–Lusztig varieties. This conjecture provides a powerful tool to determine decomposition numbers of unipotent ?-blocks of finite reductive groups.