Elliptic zastava. (English) Zbl 1523.14025
Summary: We study the elliptic zastava spaces, their versions (twisted, Coulomb, Mirković local spaces, reduced) and relations with monowalls moduli spaces and Feigin-Odesskiĭ moduli spaces of \(G\)-bundles with parabolic structure on an elliptic curve.
MSC:
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 14D20 | Algebraic moduli problems, moduli of vector bundles |
| 14H60 | Vector bundles on curves and their moduli |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
References:
| [1] | Braverman, Alexander, Semi-infinite Schubert varieties and quantum \(K\)-theory of flag manifolds, J. Amer. Math. Soc., 1147-1168 (2014) · Zbl 1367.17011 · doi:10.1090/S0894-0347-2014-00797-9 |
| [2] | Braverman, Alexander, Gaiotto-Witten superpotential and Whittaker D-modules on monopoles, Adv. Math., 451-472 (2016) · Zbl 1383.14012 · doi:10.1016/j.aim.2016.03.024 |
| [3] | A. Braverman, M. Finkelberg, D. Gaitsgory, and I. Mirkovi\'c, Intersection cohomology of Drinfeld’s compactifications, Selecta Math.(N.S.) 8 (2002), no. 3, 381-418; and Erratum, Selecta Math.(N.S.) 10 (2004), 429-430. · Zbl 1063.14503 |
| [4] | Braverman, Alexander, Towards a mathematical definition of Coulomb branches of 3-dimensional \(\mathcal N=4\) gauge theories, II, Adv. Theor. Math. Phys., 1071-1147 (2018) · Zbl 1479.81043 · doi:10.4310/ATMP.2018.v22.n5.a1 |
| [5] | Braverman, Alexander, Coulomb branches of \(3d \mathcal N=4\) quiver gauge theories and slices in the affine Grassmannian, Adv. Theor. Math. Phys., 75-166 (2019) · Zbl 1479.81044 · doi:10.4310/ATMP.2019.v23.n1.a3 |
| [6] | Cherkis, Sergey, Nahm transform for periodic monopoles and \(\mathcal{N}=2\) super Yang-Mills theory, Comm. Math. Phys., 333-371 (2001) · Zbl 1003.53025 · doi:10.1007/PL00005558 |
| [7] | Cherkis, Sergey A., Moduli of monopole walls and amoebas, J. High Energy Phys., 090, front matter+36 pp. (2012) · Zbl 1348.81313 · doi:10.1007/JHEP05(2012)090 |
| [8] | V. Drinfeld, Grinberg-Kazhdan theorem and Newton groupoids, 1801.01046, 2018. |
| [9] | Fe\u{\i }gin, B. L., Topics in quantum groups and finite-type invariants. Vector bundles on an elliptic curve and Sklyanin algebras, Amer. Math. Soc. Transl. Ser. 2, 65-84 (1998), Amer. Math. Soc., Providence, RI · Zbl 0916.16014 · doi:10.1090/trans2/185/04 |
| [10] | M. Finkelberg, A. Kuznetsov, N. Markarian, and I. Mirkovi\'c, A note on a symplectic structure on the space of \(G\)-monopoles, Commun. Math. Phys. 201 (1999), 411-421; and Erratum, Commun. Math. Phys. 334 (2015), 1153-1155. · Zbl 0981.53083 |
| [11] | Finkelberg, Michael, Towards a cluster structure on trigonometric zastava, Selecta Math. (N.S.), 187-225 (2018) · Zbl 1423.13122 · doi:10.1007/s00029-016-0287-1 |
| [12] | R. Friedman and J. W. Morgan, Holomorphic principal bundles over elliptic curves, math/9811130, 1998. |
| [13] | Friedman, Robert, Principal \(G\)-bundles over elliptic curves, Math. Res. Lett., 97-118 (1998) · Zbl 0937.14019 · doi:10.4310/MRL.1998.v5.n1.a8 |
| [14] | Feigin, Evgeny, Semi-infinite Pl\"{u}cker relations and Weyl modules, Int. Math. Res. Not. IMRN, 4357-4394 (2020) · Zbl 1476.14082 · doi:10.1093/imrn/rny121 |
| [15] | Finkelberg, Michael, Representations and nilpotent orbits of Lie algebraic systems. Multiplicative slices, relativistic Toda and shifted quantum affine algebras, Progr. Math., 133-304 (2019), Birkh\"{a}user/Springer, Cham |
| [16] | V. Ginzburg, M. Kapranov, and E. Vasserot, Elliptic algebras and equivariant cohomology I, q-alg/9505012, 1995. |
| [17] | Gaitsgory, D., Twisted Whittaker model and factorizable sheaves, Selecta Math. (N.S.), 617-659 (2008) · Zbl 1160.17009 · doi:10.1007/s00029-008-0053-0 |
| [18] | Ganter, Nora, The elliptic Weyl character formula, Compos. Math., 1196-1234 (2014) · Zbl 1300.55008 · doi:10.1112/S0010437X1300777X |
| [19] | Grojnowski, I., Elliptic cohomology. Delocalised equivariant elliptic cohomology, London Math. Soc. Lecture Note Ser., 114-121 (2007), Cambridge Univ. Press, Cambridge · Zbl 1236.55008 · doi:10.1017/CBO9780511721489.007 |
| [20] | Hua, Zheng, Shifted Poisson structures and moduli spaces of complexes, Adv. Math., 991-1037 (2018) · Zbl 1400.53070 · doi:10.1016/j.aim.2018.09.018 |
| [21] | Jarvis, Stuart, Euclidean monopoles and rational maps, Proc. London Math. Soc. (3), 170-192 (1998) · Zbl 0893.53010 · doi:10.1112/S0024611598000434 |
| [22] | Jarvis, Stuart, Construction of Euclidean monopoles, Proc. London Math. Soc. (3), 193-214 (1998) · Zbl 0893.53011 · doi:10.1112/S0024611598000446 |
| [23] | I. Mirkovi\'c, Y. Yang, and G. Zhao, Loop Grassmannians of quivers and affine quantum groups, 1810.10095, 2018. |
| [24] | H. Nakajima and A. Weekes, Coulomb branches of quiver gauge theories with symmetrizers, 1907.06552, 2019. |
| [25] | Pantev, Tony, Shifted symplectic structures, Publ. Math. Inst. Hautes \'{E}tudes Sci., 271-328 (2013) · Zbl 1328.14027 · doi:10.1007/s10240-013-0054-1 |
| [26] | Polishchuk, Alexander, Abelian varieties, theta functions and the Fourier transform, Cambridge Tracts in Mathematics, xvi+292 pp. (2003), Cambridge University Press, Cambridge · Zbl 1018.14016 · doi:10.1017/CBO9780511546532 |
| [27] | Safronov, Pavel, Poisson-Lie structures as shifted Poisson structures, Adv. Math., Paper No. 107633, 68 pp. (2021) · Zbl 1482.17052 · doi:10.1016/j.aim.2021.107633 |
| [28] | Schieder, Simon, The Harder-Narasimhan stratification of the moduli stack of \(G\)-bundles via Drinfeld’s compactifications, Selecta Math. (N.S.), 763-831 (2015) · Zbl 1341.14006 · doi:10.1007/s00029-014-0161-y |
| [29] | T. Spaide, Shifted symplectic and Poisson structures on spaces of framed maps, 1607.03807, 2016. |
| [30] | Zhu, Xinwen, Affine Demazure modules and \(T\)-fixed point subschemes in the affine Grassmannian, Adv. Math., 570-600 (2009) · Zbl 1167.14033 · doi:10.1016/j.aim.2009.01.003 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
