Christian Korff
A Combinatorial Derivation of the Racah-Speiser Algorithm for Gromov-Witten invariants.
Tue, 10/20/2009 - 12:53 — SomNambulAuthors: Christian Korff
Subjects: Representation Theory
AbstractUsing a finite-dimensional Clifford algebra a new combinatorial product
formula for the small quantum cohomology ring of the complex Grassmannian is
presented. In particular, Gromov-Witten invariants can be expressed through
certain elements in the Clifford algebra, this leads to a q-deformation of the
Racah-Speiser algorithm allowing for their computation in terms of Kostka
numbers. The second main result is a simple and explicit combinatorial formula
for projecting product expansions in the quantum cohomology ring onto the sl(n)
Verlinde algebra.The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology.
Tue, 09/15/2009 - 11:27 — SomNambulAuthors: Christian Korff, Catharina Stroppel
Subjects: Representation Theory
AbstractA simple, combinatorial construction of the sl(n)-WZNW fusion ring, also
known as Verlinde algebra, is given. As a byproduct of the construction one
obtains an isomorphism between the fusion ring and a particular quotient of the
small quantum cohomology ring of the Grassmannian Gr(k,k+n). We explain how our
approach naturally fits into known combinatorial descriptions of the quantum
cohomology ring, by establishing what one could call a
`Boson-Fermion-correspondence' between the two rings.
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