Speaker: Francois Bergeron, Universite du Quebec a Montreal
Time:    Friday, April 11, 10:00 am
Place:   room: STE 1010, University of Ottawa
Title:   Diagonal Alternants.

Abstract: We consider, on the space of polynomials in $2 n$ variables
$X=x_1,\ldots,x_n$ and $Y=y_1,\ldots,y_n$, the usual action of the group
$S_n\times S_n$. Using a classical result of Steinberg, this space $Q[X,Y]$
can be viewed as a $n!^2$ dimensional module over the invariants of the
group. This is to say that polynomials in X and Y can be uniquely decomposed
as linear expressions in covariants, with coefficients that are invariants.
We use theses results, together with restriction to $S_n$ (considered 
as a diagonal subgroup), to decompose diagonal alternants. We give
an explicit basis for diagonal alternants, modulo the ideal generated by
products of symmetric polynomials in $X$ and $Y$. The construction of 
thisbasis involves a very nice classification of configurations on $n$ 
points in $R^2$.