Recently, V. Ginzburg proved that Calogero phase space is a coad-joint orbit for some innnite dimensional Lie algebra coming from noncommuta-tive symplecticgeometry, 8]. In this note we generalize his argument to speciic quotient varieties of representations of (deformed) preprojective algebras. This result was also obtained independently by V. Ginzburg 9]. Using results of W. Crawley-Boevey an...

After reviewing the D-branes as a conjugacy classes and various charge quantization (modulo k) in WZW model, we develop the classification and systematic construction of all possible untwisted D-branes in Lie groups of A-D-E series. Dbranes are classified according to their positions in the maximal torus. The moduli space of D-branes is naturally identified with unit cell in the weight space wh...

We study to which extent the family of pairs of subspaces of a vector space related to each other via intersection properties determines the vector space. In another language, we study to which extent the family of vertices of the building of a projective space related to each other via several natural respective conditions involving the Weyl distance and incidence determines the building. Thes...

We propose a continuous Wick rotation for Dirac, Majorana and Weyl spinors from Minkowski spacetime to Euclidean space which treats fermions on the same footing as bosons. The result is a recipe to construct a supersymmetric Euclidean theory from any supersymmetric Minkowski theory. This Wick rotation is identified as a complex Lorentz boost in a five-dimensional space and acts uniformly on bos...

We study the theory of Weyl conformal gravity with matter degrees of freedom in a conformally invariant interaction. Specifically, we consider a triplet of scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model conformally coupled to Weyl gravity. We show that the equations of motion admit solutions spontaneously breaking the conformal symmetry and the gauge symmetry, p...