School Seminars and Colloquia

su(N) tensor-product multiplicities as polytope volumes

Mathematical Physics Seminar

by Jorgen Rasmussen

Institution: University of Melbourne
Date: Thu 20th October 2005
Time: 2:15 PM
Location: Theatre 1, Old Geology Building, The University of Melbourne

Abstract: Information on su(N) tensor-product multiplicities is neatly
encoded in the so-called Berenstein-Zelevinsky (BZ) triangles.
The multiplicities for given highest-weight modules are given simply
by the number of allowed BZ triangles associated to these modules.
This illustrates the vital role combinatorics plays in the theory
of highest-weight modules of Lie algebras.
While this talk concerns an explicit formula for these multiplicities,
it only assumes very basic knowledge on the problem.
By relaxing one of the conditions in the definition of the BZ triangles,
one may introduce virtual BZ triangles, enabling
one to characterize a tensor-product multiplicity as the number of integer
points in a convex polytope. It turns out that this discretized volume
can be evaluated explicitly as a multiple sum.

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