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Abstract We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and enriched Schubert polynomials. We also construct an embedding of the type C flag variety and study the corresponding pullback map on (equivariant) cohomology rings.
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On the smooth locus of affine Schubert varieties
Abstract We give a simple and uniform proof of a conjecture of Haines–Richarz characterizing the smooth locus of Schubert varieties in twisted affine Grassmannians. Our method is elementary and avoids any representation theoretic techniques, instead relying on a combinatorial analysis of tangent spaces of Schubert varieties.
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- Award ID(s):
- 2100743
- PAR ID:
- 10576986
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Mathematische Annalen
- Volume:
- 392
- Issue:
- 2
- ISSN:
- 0025-5831
- Format(s):
- Medium: X Size: p. 1483-1501
- Size(s):
- p. 1483-1501
- Sponsoring Org:
- National Science Foundation
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