The symmetric functions catalog

2023-09-20

Kohnert polynomials

Kohnert polynomials were introduced by Assaf and Searles in [AS22b]. This is a large family of polynomials, which contains several of the classical families as special cases, in particular the family of Schubert polynomials and key polynomials.

All Kohnert polynomials are monomial slide positive, [Thm. 3.7, AS22b], and they were later proved to be key positive in [Ass21].

See [AABE23] for a representation-theoretical interpretation of Kohnert polynomials.

References

• [AABE23] Sam Armon, Sami Assaf, Grant Bowling and Henry Ehrhard. Kohnert's rule for flagged Schur modules. Journal of Algebra, 617:352–381, March 2023.
• [AS22b] Sami Assaf and Dominic Searles. Kohnert polynomials. Experimental Mathematics, 31(1):93–119, April 2022.
• [Ass21] Sami Assaf. Demazure crystals for Kohnert polynomials. Transactions of the American Mathematical Society, 375(3):2147–2186, December 2021.