208 research outputs found
The endomorphism of Grassmann graphs
A graph is called a pseudo-core if every endomorphism is either an
automorphism or a colouring. In this paper, we show that every Grassmann graph
is a pseudo-core. Moreover, the Grassmann graph is a core
whenever and are not relatively prime, and is a
core whenever .Comment: 8 page
Semidefinite programming, harmonic analysis and coding theory
These lecture notes where presented as a course of the CIMPA summer school in
Manila, July 20-30, 2009, Semidefinite programming in algebraic combinatorics.
This version is an update June 2010
Gauge Theory for Spectral Triples and the Unbounded Kasparov Product
We explore factorizations of noncommutative Riemannian spin geometries over
commutative base manifolds in unbounded KK-theory. After setting up the general
formalism of unbounded KK-theory and improving upon the construction of
internal products, we arrive at a natural bundle-theoretic formulation of gauge
theories arising from spectral triples. We find that the unitary group of a
given noncommutative spectral triple arises as the group of endomorphisms of a
certain Hilbert bundle; the inner fluctuations split in terms of connections
on, and endomorphisms of, this Hilbert bundle. Moreover, we introduce an
extended gauge group of unitary endomorphisms and a corresponding notion of
gauge fields. We work out several examples in full detail, to wit Yang--Mills
theory, the noncommutative torus and the -deformed Hopf fibration over
the two-sphere.Comment: 50 pages. Accepted version. Section 2 has been rewritten. Results in
sections 3-6 are unchange
Verma modules and preprojective algebras
We give a geometric construction of the Verma modules of a symmetric
Kac-Moody Lie algebra in terms of constructible functions on the varieties of
nilpotent finite-dimensional modules of the corresponding preprojective
algebra.Comment: Minor changes. Final version. To appear in Nagoya Math. Journa
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