Polyhedral expressions for generalized Littlewood-Richardson coefficients

Andrei Zelevinsky

Northeastern University

February 18,
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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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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