{TALK 
        {"October 14}
        {"Quadratic relations among characters}
        {"Michael Kleber}
        {"MIT}
        {"kleber@math.mit.edu}
        {"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.
}
}