@article{7683,
abstract = {For any free oriented Borel–Moore homology theory A, we construct an associative product on the A-theory of the stack of Higgs torsion sheaves over a projective curve C. We show that the resulting algebra AHa0C admits a natural shuffle presentation, and prove it is faithful when A is replaced with usual Borel–Moore homology groups. We also introduce moduli spaces of stable triples, heavily inspired by Nakajima quiver varieties, whose A-theory admits an AHa0C-action. These triples can be interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action of AHa0C on the cohomology of Hilbert schemes of points on T∗C.},
author = {Minets, Sasha},
issn = {14209020},
journal = {Selecta Mathematica, New Series},
number = {2},
publisher = {Springer Nature},
title = {{Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces}},
doi = {10.1007/s00029-020-00553-x},
volume = {26},
year = {2020},
}
@article{7940,
abstract = {We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras. As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay, Regelskis, and Wendlandt [GRW18].},
author = {Yang, Yaping and Zhao, Gufang},
issn = {1531586X},
journal = {Transformation Groups},
publisher = {Springer Nature},
title = {{The PBW theorem for affine Yangians}},
doi = {10.1007/s00031-020-09572-6},
year = {2020},
}
@article{439,
abstract = {We count points over a finite field on wild character varieties,of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras. Our result leads to the conjecture that the mixed Hodge polynomials of these character varieties agree with previously conjectured perverse Hodge polynomials of certain twisted parabolic Higgs moduli spaces, indicating the
possibility of a P = W conjecture for a suitable wild Hitchin system.},
author = {Hausel, Tamas and Mereb, Martin and Wong, Michael},
issn = {1435-9855},
journal = {Journal of the European Mathematical Society},
number = {10},
pages = {2995--3052},
publisher = {European Mathematical Society},
title = {{Arithmetic and representation theory of wild character varieties}},
doi = {10.4171/JEMS/896},
volume = {21},
year = {2019},
}
@article{441,
author = {Kalinin, Nikita and Shkolnikov, Mikhail},
issn = {2199-6768},
journal = {European Journal of Mathematics},
number = {3},
pages = {909–928},
publisher = {Springer Nature},
title = {{Tropical formulae for summation over a part of SL(2,Z)}},
doi = {10.1007/s40879-018-0218-0},
volume = {5},
year = {2019},
}
@article{5,
abstract = {In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix coefficients, and from its realization as a GIT quotient of the Vinberg semigroup. In order to define the wonderful compactification for a quantum group, we adopt a generalized formalism of Proj categories in the spirit of Artin and Zhang. Key to our construction is a quantum version of the Vinberg semigroup, which we define as a q-deformation of a certain Rees algebra, compatible with a standard Poisson structure. Furthermore, we discuss quantum analogues of the stratification of the wonderful compactification by orbits for a certain group action, and provide explicit computations in the case of SL2.},
author = {Ganev, Iordan V},
journal = {Journal of the London Mathematical Society},
number = {3},
pages = {778--806},
publisher = {Wiley},
title = {{The wonderful compactification for quantum groups}},
doi = {10.1112/jlms.12193},
volume = {99},
year = {2019},
}