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Elliptic stable envelopes

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arxiv 1604.00423 v4 pith:K3FA3TN4 submitted 2016-04-01 math.AG hep-thmath-phmath.MPmath.RT

Mina Aganagic , Andrei Okounkov This is my paper · ORCID
classification math.AGhep-thmath-phmath.MPmath.RT
keywords ellipticenvelopesequationsnakajimastablevarietiesapplyarising
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abstract

We construct stable envelopes in equivariant elliptic cohomology of Nakajima quiver varieties. In particular, this gives an elliptic generalization of the results of arXiv:1211.1287. We apply them to the computation of the monodromy of $q$-difference equations arising the enumerative K-theory of rational curves in Nakajima varieties, including the quantum Knizhnik-Zamolodchikov equations.

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  1. $Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory

    hep-th 2025-07 conditional novelty 7.0 of 10

    In 5d N=1 U(N) gauge theory, codimension-two defects produce Q-operators whose q-difference equations are the Baxter TQ equations of XXZ spin chains built on bi-infinite evaluation modules of quantum affine algebras.

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