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In this paper we give a brief account of the main aspects of the theory of associated and principal super bundles. As an application, we review the Borel-Weil-Bott Theorem in the super setting, and some results on projective embeddings of homogeneous spaces.
We address the construction of smooth bundles of fermionic Fock spaces, a problem that appears frequently in fermionic gauge theories. Our main motivation is the spinor bundle on the free loop space of a string manifold, a structure anticipated by Ki
We study the Ext modules in the category of left modules over a twisted algebra of a finite quiver over a ringed space $(X,mathcal O_X)$, allowing for the presence of relations. We introduce a spectral sequence which relates the Ext modules in that c
We review the list of non-degenerate invariant (super)symmetric bilinear forms (briefly: NIS) on the following simple (relatives of) Lie (super)algebras: (a) with symmetrizable Cartan matrix of any growth, (b) with non-symmetrizable Cartan matrix of
In a previous article the second author together with A. Pasquale determined the spectrum of the $Cos^lambda$ transform on smooth functions on the Grassmann manifolds $G_{p,n+1}$. This article extends those results to line bundles over certain Grassm
Using Szenes formula for multiple Bernoulli series we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also certain multiple zeta values.