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

Darij Grinberg

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

Combinatorics 2026-05-27 v1 Number Theory Rings and Algebras

Authors: Darij Grinberg

Abstract

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.

Keywords

schubert polynomials macdonald polynomials

Cite

@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}
}

Comments

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

Abstract

Keywords

Cite

Comments

Related papers