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

Abstract

We generalize and prove the recursive relation \[ S_λ(V) = \sum_{L\subseteq V\text{ line}} S_λ(V \mathbin{/\mkern-5mu/} L) \] 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.

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! v2 adds a reference to a parallel development of the same results