Weyl group

For the application of Theorem 6.8 to the Springer representation of the Weyl group, we refer to [10]. Another interesting application to the representation theory was given in [12]. 

The convergence of this method can be argued along the same lines as in the case of usual collision theory (see for instance B. Weyl Group Theory and Quantum Mechanics 2nd Ed., 1931, p. 63), and we can show that the expansion (33) can be expressed (majorisieren) by a geometric series in the case where... 

H. Weyl, Space, Time, Matter, Dover Books, New York, 1950 The Theory of Groups and Quantum Mechanics, Dover Books, New York, 1950. 

Ring enlargement via an insertion of a carbene generated in the a-position to the ring is an established method and has also been applied to the synthesis of oxepins. The ()3-allylpalladium chloride catalyzed decomposition of substituted ethyl diazo(4/7-pyran-4-yl)acetates in benzene at room temperature gives ethyl oxepin-4-carboxylates 1 in excellent yield.190 The ester function can be replaced by the phosphonate group and other P = 0-functions (see Houben-Weyl,... 

Oxidation of diethyl 3,6-hexanooxepin-4,5-dicarboxylate with ruthenium(VIII) oxide, generated from ruthenium(III) chloride and sodium periodate in situ, gives the corresponding hexa-no-bridged furan 1 a with loss of two carbon atoms (see Houben-Weyl, Vol. E6a, p 77).200 201 One of the central methylene groups can be replaced by a carbonyl group to give lb.200... 

The 1-benzoyl-l//-l,2-diazepines 3 undergo loss of the A -benzoyl group and ring contraction to provide the pyridines 4 in refluxing xylene (see Houben-Weyl, Vol. E7b, p 519).93... 

D.1.3. Formation of C —C Bonds by Addition to Carbonyl Groups Houben-Weyl... 

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