Macaulay2 » Documentation
Packages » SchurRings :: scalarProduct
next | previous | forward | backward | up | index | toc

scalarProduct -- Standard pairing on symmetric functions/class functions


This method computes the standard scalar product on the ring \Lambda of symmetric functions. One way to define this product is by imposing that the collection of Schur functions s_{\lambda} form an orthonormal basis.

Alternatively, by the correspondence between symmetric functions and virtual characters of symmetric groups, this scalar product coincides with the standard scalar product on class functions.

The number of standard tableaux of shape \{4,3,2,1\} is:

i1 : R = symmetricRing(QQ,10);
i2 : S = schurRing(QQ,s,10);
i3 : scalarProduct(h_1^10,s_{4,3,2,1})

o3 = 768

o3 : QQ

See also

Ways to use scalarProduct :

For the programmer

The object scalarProduct is a method function.