Abstracts for MPI-Oberseminar

We introduce a new algebra, which can be regarded as a mixture of the
tensor algebra and the infinite symmetric group.  As basic operators  on
this algebra, we can consider "multiplications" by vectors and
"derivations" by convectors.  These two types of operators satisfy an
analogue of the canonical commutation relations, and we can regard the
operator algebra generated by these as an analogue of the Weyl algebra  and
the Clifford algebra.  These algebras have applications to  noncommutative

The isomonodromic deformation equations, which form the main stream of the evolution of the modern theory of special functions, may be associated with some algebraic Hamiltonian system. The Hamiltonian system is defined on the space that is the symplectic quotient of the product of the several coadjoint orbits. These spaces are the subject of our investigations.

Let X be a symmetric space of noncompact type (e.g. SL(n)/SO(n)) or a thick Euclidean bulding. We will discuss following geometric question: which are the possible side lengths of polygons in X?
The full invariant of an oriented geodesic segment in a symmetric space X=G/K modulo the action of G is a vector in \R^{rank(X)}. Thus in our context the appropriate notion of length is given by this vector. The same notion of vector valued length can be defined for Euclidean buildings.

Affine Hecke algebras are algebras defined as a deformation of affine Weyl
groups. Though it does not have equivalent representation theory as that of
affine Weyl groups, it inherits many structures from the counter-part of
affine Weyl groups.

In this talk, I will explain how the Specht construction (a classical
famous realization of irreducible representations of symmetric groups) fit
into the representation theory of affine Hecke algebras of classical types,
in a way it gives "standard modules" in some sense. This view point has