Quadratic relations among characters
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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