Stable envelopes were introduced by Maulik and Okounkov in cohomology, then by Okounkov and Smirnov in K-theory, to provide geometric constructions of R-matrices with spectral parameters (among other applications, such as in enumerative geometry). In the cohomology case this story applies to Yangians, while the K-theory case is concerned with quantum affine algebras. In this talk we will introduce stable envelopes in the context of equivariant K-theory of Nakajima quiver varieties. We will then see how they can be applied to studying quantum affine algebras, building to the definition of the so called Maulik-Okounkov quantum affine algebra.

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