The V/L recursion for Macdonald's 7th Variation Schur polynomials

Darij Grinberg

The V/L recursion for Macdonald's 7th Variation Schur polynomials

组合数学 2026-05-27 v1 数论环与代数

作者: Darij Grinberg

摘要

We generalize and prove the recursive relation $S_{\lambda}(V) = \sum_{L\subseteq V\text{ line}} S_{\lambda}(V \mathbin{/\mkern-5mu/} L)$ conjectured by I. G. Macdonald for his "7th variation" of the Schur functions. This variation is a family of polynomials over a finite field that mimic the (straight and skew) Schur polynomials using powers of the Frobenius.

关键词

schubert polynomials macdonald polynomials

引用

@article{arxiv.2605.26775,
  title  = {The V/L recursion for Macdonald's 7th Variation Schur polynomials},
  author = {Darij Grinberg},
  journal= {arXiv preprint arXiv:2605.26775},
  year   = {2026}
}

备注

47 pages, of which the first 21 prove the main result. Includes some exposition. Errata for Macdonald's original paper, with some more omitted details, are included as ancillary file. Comments are welcome!

The V/L recursion for Macdonald's 7th Variation Schur polynomials

摘要

关键词

引用

备注

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