2025/10/12 by Lu, Kang, Wang, Weiqiang, Weekes, Alex · 4 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2510.10652
In a prequel we introduced the shifted iYangians ^\imath Yμ associated to quasi-split Satake diagrams of type ADE and even spherical coweights μ, and constructed the iGKLO representations of ^\imath Yμ, which factor through truncated shifted iYangians ^\imath Yμλ. In this paper, we show that ^\imath Yμ quantizes the involutive fixed point locus ^\imath Wμ arising from affine Grassmannians of type ADE, and supply strong evidence toward the expectation that ^\imath Yμλ quantizes a top-dimensional component of the affine Grassmannian islice ^\imathWμλ. We identify the islices ^\imathWμλ in type AI with suitable nilpotent Slodowy slices of type BCD, building on the work of Lusztig and Mirković-Vybornov in type A. We propose a framework for producing ortho-symplectic (and hybrid) Coulomb branches from split (and nonsplit) Satake framed double quivers, which are conjectured to relate closely to the islices ^\imathWμλ and the algebras ^\imath Yμλ.