MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
show/hide this revision's text 2 now 0<=i<e, 0<=j<d

I'm just curious about the polynomial $\det (x_k^iy_k^j)_{1\leq x_k^iy_k^j)_{0\leq i\leq dd-1, 1\leq 0\leq j\leq ee-1, 1\leq k\leq de}$ (determinant of $de\times de$-matrix, $x_k$, $y_k$ are all independent variables). Is anything known about its factorization on irreducible polynomials?

The question is based only on my own interest.
show/hide this revision's text 1

Is this polynomial irreducible?

I'm just curious about the polynomial $\det (x_k^iy_k^j)_{1\leq i\leq d, 1\leq j\leq e, 1\leq k\leq de}$ (determinant of $de\times de$-matrix, $x_k$, $y_k$ are all independent variables). Is anything known about its factorization on irreducible polynomials?

The question is based only on my own interest.