Quadratic relations among characters

Michael Kleber


October 14,
refreshments at 3:45pm


There is a remarkable set of quadratic relations among the characters of representations of gl(n) corresponding to rectangular Young diagrams, which can be derived from the Littlewood-Richardson rule. Generalizing these relations cleverly to Lie algebras of types B-C-D (for Lie theorists), it appears we are really looking at characters of the associated quantum affine algebras. These relations led to the study of "rigged configurations" (for combinatorialists) and some new formulas for decomposing tensor products of rectangles. A recent result shows that the relations actually determine the quantum characters of rectangles, and there is some hope that this can be generalized to other characters.

Speaker's Contact Info: kleber(at-sign)math.mit.edu

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

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