Polyhedral expressions for generalized Littlewood-Richardson
refreshments at 3:45pm
In a joint work with Arkady Berenstein, a family of explicit
"polyhedral" combinatorial expressions is given for
multiplicities in the tensor product of two simple
finite-dimensional modules over a complex semisimple Lie algebra.
Here "polyhedral" means that the multiplicity in question is
expressed as the number of lattice points in some convex polytope.
Our answers use a new combinatorial concept of i-trails which
resemble Littelmann's paths but seem to be more tractable. We also
study combinatorial structure of Lusztig's canonical bases or,
equivalently of Kashiwara's global bases. Although Lusztig's and
Kashiwara's approaches were shown by Lusztig to be equivalent to
each other, they lead to different combinatorial parametrizations
of the canonical bases. One of our main results is an explicit
description of the relationship between these parametrizations.
Speaker's Contact Info: andrei(at-sign)neu.edu
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