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weylNormalize -- sort each row of a WeylFilling into weakly-increasing order

Description

Each row of a WeylFilling represents a basis element $x^{(a_1)} x^{(a_2)} \cdots \in D^\ell(E)$ of a divided power. Divided powers of a free module have a basis indexed by unordered multisets of basis indices (or, equivalently, exponent vectors), so two WeylFillings with the same multiset of entries in each row represent the same element of the ambient. weylNormalize puts every row into its canonical sorted representative.

Unlike normalize on the Schur side, no sign is produced: divided powers are cocommutative / symmetric, not alternating.

i1 : U = new WeylFilling from {{2,0,1}, {3,1}}

     +-+-+-+
o1 = |2|0|1|
     |3|1| |
     +-+-+-+

o1 : WeylFilling
i2 : weylNormalize U

     +-+-+-+
o2 = |0|1|2|
     |1|3| |
     +-+-+-+

o2 : WeylFilling

See also

Ways to use weylNormalize:

  • weylNormalize(WeylFilling)

For the programmer

The object weylNormalize is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SchurFunctors.m2:1664:0.