Equivariant Cohomology in Algebraic Geometry Lecture Eight: Equivariant Cohomology of Grassmannians Ii
نویسنده
چکیده
σλ = |c T λi+j−i(Q− Fl+i−λi)|1≤i,j≤k. These determinants are variations of Schur polynomials, which we will call double Schur polynomials and denote sλ(x|y), where the two sets of variables are x = (x1, . . . , xk) and y = (y1, . . . , yn). (Here k ≤ n, and the length of λ is at most k.) Setting the y variables to 0, one recovers the ordinary Schur polynomials: sλ(x|0) = sλ(x). In fact, sλ(x|y) is symmetric in the x variables. Here we give three descriptions of these double Schur polynomials, generalizing those for ordinary Schur polynomials. Set (xi|y) p = (xi − y1)(xi − y2) · · · (xi − yp). (i) Generalizing the “bialternant” definition of Schur polynomials, we have
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