Polyhedral expressions for generalized LittlewoodRichardson
coefficients
Andrei Zelevinsky
Northeastern University
February 18,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

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
finitedimensional 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 itrails 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(atsign)neu.edu
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