Claudio 70
Titles and abstract of talks
- A life with Algebra, Claudio Procesi (Sapienza Università di Roma)
- Affine Algebras and Division Algebras, Lance Small (UCSD)
Abstract: We will survey some recent work on infinite dimensional division
algebras, their properties and how they are obtained.
- Homogeneous projective bundles over abelian varieties, Michel Brion (Institut Fourier, Grenoble)
Abstract:
We consider those projective bundles (or Brauer-Severi
varieties) over an abelian variety that are homogeneous,
i.e., invariant under translation. We describe the
structure of these bundles in terms of projective
representations of commutative group schemes; the
irreducible bundles correspond to Heisenberg groups and
their standard representations. Our results extend those
of Mukai on semi-homogeneous vector bundles, and yield
a geometric view of the Brauer group of abelian varieties.
- Construction of
semisimple tensor categories,
Friedrich Knop (Erlangen University)
Abstract. Deligne constructed a tensor category Rep(S_t), where t is an
arbitrary parameter, which can be interpreted as an interpolation of
the categories of representations of the symmetric groups S_n. We report
on a generalization of this result and on some more recent results on
Deligne's category.
- Conjugacy classes in the Weyl group and unipotent classes, George Lusztig (MIT)
Abstract:
A natural surjective map from the set of
conjugacy classes in the Weyl group to the set of unipotent classes
in a reductive group is constructed.
- Macdonald and LLT polynomials, Mark Haiman (University of California)
Abstract:
Some years ago, inspired by Claudio's ideas, I worked out a
connection between the theory of Macdonald polynomials and the
geometry of Hilbert schemes of points in the plane. Since that time,
the study from a more combinatorial point of view has revealed another
deep connection, between Macdonald polynomials and LLT polynomials.
The main goal of my talk will be to explain the latter. I will also
try to say something about the possibility that all three things are
connected.
- Cohomology of line bundles for Sp(4), Stephen Donkin (University of York)
Abstract: At Claudio Procesi's 60th Birthday Conference I discussed a recursive procedure for determining the cohomology of line bundles in characteristic p>0. Subsequently this was applied to SL(3) and recursive formulas for the characters of cohomology groups given. As well as the line bundles the recursions involves (very natural) rank 2 bundles. In the case of Sp(4) several new features emerge and one has to deal with some extra vector bundles and apply new tricks.
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Reduced invariant sets,
Gerald Schwarz (Brandeis University)
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Affine Space Fibrations and Bundles: Another Challenge for Affine n-Space, Hanspeter Kraft (University of Basel)