Schubert line defects in 3d GLSMs for complete flag manifolds are realized as SQM quivers whose indices give quantum Grothendieck polynomials and restrict the target space to Schubert varieties.
Grothendieck polynomials and quiver formulas
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abstract
Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear combinations of products of stable Grothendieck polynomials. We prove an explicit combinatorial formula for the coefficients, which shows that they have alternating signs. Our result is applied to obtain new expansions for the Grothendieck polynomials of Lascoux and Sch\"utzenberger.
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Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials
Schubert line defects in 3d GLSMs for complete flag manifolds are realized as SQM quivers whose indices give quantum Grothendieck polynomials and restrict the target space to Schubert varieties.