Moscow Mathematical Journal

Volume 21, Issue 1, January–March 2021 pp. 191–226.

Schubert Polynomials, Theta and Eta Polynomials, and Weyl Group Invariants

Authors: Harry Tamvakis (1)
Author institution:University of Maryland, Department of Mathematics, William E. Kirwan Hall, 4176 Campus Drive, College Park, MD 20742, USA (1)

Summary:

We examine the relationship between the (double) Schubert polynomials of Billey–Haiman and Ikeda–Mihalcea–Naruse and the (double) theta and eta polynomials of Buch–Kresch–Tamvakis and Wilson from the perspective of Weyl group invariants. We obtain generators for the kernel of the natural map from the corresponding ring of Schubert polynomials to the (equivariant) cohomology ring of symplectic and orthogonal flag manifolds.

2010 Math. Subj. Class. Primary: 14M15; Secondary: 05E05, 13A50, 14N15.

Keywords: Schubert polynomials, theta and eta polynomials, Weyl group invariants, flag manifolds, equivariant cohomology.

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