2018

Quiver varieties and symmetric pairs

Li, Yiqiang

Understand

We study fixed-point loci of Nakajima varieties under symplectomorphisms and their anti-symplectic cousins, which are compositions of a diagram automorphism, a reflection functor and a transpose defined by certain bilinear forms.

These subvarieties provide a natural home for geometric representation theory of symmetric pairs.
In particular, the cohomology of a Steinberg-type variety of the symplectic fixed-point subvarieties is conjecturally related to the universal enveloping algebra of the subalgebra in a symmetric pair.
The latter symplectic subvarieties are further used to construct geometrically an action of a twisted Yangian on torus equivariant cohomology of Nakajima varieties.

Built on

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Then

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S. Kolb, Quantum symmetric Kac-Moody pairs
2014
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E. Briand, R. Orellana and M. Rosas, Rectangular symmetries for coefficients of symmetric functions
2015
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A. Henderson, Singularities of nilpotent orbit closures
2015
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M.Balagovic and S. Kolb, Universal K-matrix for quantum symmetric pairs
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H. Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories, I
Original
2016
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H. Bao and W. Wang, A new approach to Kazhdan-Lusztig theory of type B B via quantum symmetric pairs
2018
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H. Bao and W. Wang, Canonical bases arising from quantum symmetric pairs
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N. Guay, V. Regelskis and C. Wendlandt, Representations of twisted Yangians of types B, C, D: I
2071
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