Motivated by the physical concept of special geometry, two mathematical constructions are studied which relate real hypersurfaces to tube domains and complex Lagrangian cones, respectively.
The theory is applied to the case of cubic hypersurfaces, which is the one most relevant to special geometry, obtaining the solution of the two classification problems and the description of the corresponding homogeneous special K?hler manifolds.
Recently, there is a renewed interest in wonderful varieties of rank two since they were shown to hold a keystone position in the theory of spherical varieties, see [L], [BP], and [K].
We apply this criterion of algebraic integrability to two examples: finite-zone potentials and the elliptic Calogero-Moser system.
There are two well known combinatorial tools in the representation theory ofSLn, the semi-standard Young tableaux and the Gelfand-Tsetlin patterns.
In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
A local-global principle is proved by the second named author in the adjacent paper of this volume.
In the second part we apply this method to obtain pseudo-Riemannian homogeneous manifolds with real Killing spinors.
We derive two consequences: the first is a new proof of Lusztig's description of the intersection cohomology of nilpotent orbit closures for GLn, and the second is an analogous description for GL2n/Sp2n.
The second part consists in the normalization of the Burkhardt dual.
Design, Synthesis and Growth Inhibition Activity of Bis-Epoxyethyl Derivatives of Stallimycin Modified on the Amidino Moiety
We attempted to formulate quantitative structure-activity relationship modeling of 2,5-bis(1-Aziridinyl) 1,4-benzoquinone (BABQ) compounds according to calculated molecular descriptors.
A series of novel C2-symmetrical chiral bis(oxazoline) and bis(thiazoline) ligands containing noncyclic crown ether type was synthesized.
Synthesis and applications of 3,4-dihydroxy-2,5-bis-(2'-(4'-substituted-oxazolinyl)) furan
Three 3,4-dihydroxy-2,5-bis-(2'-(4'-substituted-oxazolinyl)) furans were synthesized at 90%-94% yields from reaction of 3,4-dihydroxyfuran-2,5-dicar-boxylic acid or its dimethyl ester with chiral β-amino alcohol via a one-step process.