weylCharacter -- the character of a composition of Weyl functors on GL(V)

Usage:

weylCharacter(L, d)
Inputs:
- L, a list, a list of partitions
- d, an integer, the rank of the underlying module
Outputs:
- a ring element, the character, as a symmetric polynomial in $x_0, \ldots, x_{d-1}$, of the composed Weyl functor on the defining representation

Description

The Weyl analogue of character, using weyl instead of schur. Over a field of characteristic zero $W_\lambda(V) \cong S_\lambda(V)$ canonically, so weylCharacter returns the same polynomial as character; this routine is provided for uniformity and for verifying that the diagonal-character computation goes through the Weyl-side construction end-to-end.

i1 : toString character({{2,1}}, 3) == toString weylCharacter({{2,1}}, 3)

o1 = true

i2 : splitCharacter weylCharacter({{1,1,1}, {2}}, 4)

o2 = s      + s
      4,1,1    3,3

o2 : schurRing (QQ, s, 4)

Ways to use weylCharacter:

weylCharacter(List,ZZ)

For the programmer

The object weylCharacter is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SchurFunctors.m2:2653:0.

weylCharacter -- the character of a composition of Weyl functors on GL(V)

Description

See also

Ways to use weylCharacter:

For the programmer