Hilbert schemes of nonreduced divisors in Calabi–Yau threefolds and W-algebras

citation_journal_title=Lett. Math. Phys.; citation_title=Liouville correlation functions from four-dimensional gauge theories; citation_author=LF Alday, D Gaiotto, Y Tachikawa; citation_volume=91; citation_issue=2; citation_publication_date=2010; citation_pages=167-197; citation_doi=10.1007/s11005-010-0369-5; citation_id=CR1

citation_journal_title=Invent. Math.; citation_title=Representation theory of

-algebras; citation_author=T Arakawa; citation_volume=169; citation_issue=2; citation_publication_date=2007; citation_pages=219-320; citation_doi=10.1007/s00222-007-0046-1; citation_id=CR2

Arakawa, T., Creutzig, T., Linshaw, A.R.:

$$W$$

-algebras as coset vertex algebras. Invent. Math. 218(1), 145–195 (2019).

arXiv:1801.03822

citation_title=A presentation of the deformed algebra; citation_inbook_title=Symmetries, Integrable Systems and Representations; citation_publication_date=2013; citation_pages=1-13; citation_id=CR4; citation_author=N Arbesfeld; citation_author=O Schiffmann; citation_publisher=Springer

Braverman, A., Finkelberg, M., Nakajima, H.: Instanton Moduli Spaces and

$$W$$

-Algebras. Astérisque, vol. 385. Société Mathématique de France, Paris (2016)

citation_journal_title=Doc. Math.; citation_title=Moduli of framed sheaves on projective surfaces; citation_author=U Bruzzo, D Markushevich; citation_volume=16; citation_publication_date=2011; citation_pages=399-410; citation_id=CR6

citation_journal_title=Mosc. Math. J.; citation_title=Five dimensional gauge theories and vertex operators; citation_author=E Carlsson, N Nekrasov, A Okounkov; citation_volume=14; citation_issue=1; citation_publication_date=2014; citation_pages=39-61; citation_doi=10.17323/1609-4514-2014-14-1-39-61; citation_id=CR7

citation_journal_title=Duke Math. J.; citation_title=Exts and vertex operators; citation_author=E Carlsson, A Okounkov; citation_volume=161; citation_issue=9; citation_publication_date=2012; citation_pages=1797-1815; citation_doi=10.1215/00127094-1593380; citation_id=CR8

citation_title=Representation Theory and Complex Geometry. Modern Birkhäuser Classics; citation_publication_date=2010; citation_id=CR9; citation_author=N Chriss; citation_author=V Ginzburg; citation_publisher=Birkhäuser

citation_journal_title=Q. J. Math.; citation_title=The critical CoHA of a quiver with potential; citation_author=B Davison; citation_volume=68; citation_issue=2; citation_publication_date=2017; citation_pages=635-703; citation_doi=10.1093/qmath/haw053; citation_id=CR10

Davison, B., Meinhardt, S.: Cohomological Donaldson–Thomas theory of a quiver with potential and quantum enveloping algebras. Invent. Math. 221(3), 777–871 (2020).

arXiv:1601.02479

citation_journal_title=J. Geom. Phys.; citation_title=Moduli of ADHM sheaves and local Donaldson–Thomas theory; citation_author=D-E Diaconescu; citation_volume=62; citation_issue=4; citation_publication_date=2012; citation_pages=763-799; citation_doi=10.1016/j.geomphys.2011.12.018; citation_id=CR12

Gaiotto, D., Rapčák, M.: Vertex algebras at the corner. J. High Energy Phys. 2019(1), # 160 (2019).

arXiv:1703.00982

Gholampour, A., Sheshmani, A., Yau, S.-T.: Localized Donaldson–Thomas theory of surfaces. Amer. J. Math. 142(2), 405–442 (2020).

arXiv:1701.08902

Kapranov, M., Vasserot, E.: The cohomological Hall algebra of a surface and factorization cohomology (2019).

arXiv:1901.07641

citation_journal_title=Commun. Number Theory Phys.; citation_title=Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants; citation_author=M Kontsevich, Y Soibelman; citation_volume=5; citation_issue=2; citation_publication_date=2011; citation_pages=231-352; citation_doi=10.4310/CNTP.2011.v5.n2.a1; citation_id=CR16

citation_journal_title=J. Algebraic Geom.; citation_title=Virtual pull-backs; citation_author=C Manolache; citation_volume=21; citation_issue=2; citation_publication_date=2012; citation_pages=201-245; citation_doi=10.1090/S1056-3911-2011-00606-1; citation_id=CR17

Maulik, D., Okounkov, A.: Quantum Groups and Quantum Cohomology. Astérisque, vol. 408. Société Mathématique de France, Paris (2019).

arXiv:1211.1287

Minets, A.: Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Math. (N.S.) 26(2), # 30 (2020).

arXiv:1801.01429

citation_title=Lectures on instanton counting; citation_inbook_title=Algebraic Structures and Moduli Spaces; citation_publication_date=2004; citation_pages=31-101; citation_id=CR21; citation_author=H Nakajima; citation_author=K Yoshioka; citation_publisher=American Mathematical Society

citation_journal_title=Lett. Math. Phys.; citation_title=Exts and the AGT relations; citation_author=A Neguţ; citation_volume=106; citation_issue=9; citation_publication_date=2016; citation_pages=1265-1316; citation_doi=10.1007/s11005-016-0865-3; citation_id=CR23

Neguţ, A.: AGT relations for sheaves on surfaces (2017).

arXiv:1711.00390

citation_journal_title=Comm. Math. Phys.; citation_title=The

-AGT-W relations via shuffle algebras; citation_author=A Neguţ; citation_volume=358; citation_issue=1; citation_publication_date=2018; citation_pages=101-170; citation_doi=10.1007/s00220-018-3102-3; citation_id=CR25

Nekrasov, N.: BPS/CFT correspondence II: Instantons at crossroads, moduli and compactness theorem. Adv. Theor. Math. Phys. 21(2), 503–583 (2017).

arXiv:1608.07272

Nekrasov, N., Prabhakar, N.S.: Spiked instantons from intersecting D-branes. Nucl. Phys. B 914, 257–300 (2017).

arXiv:1611.03478

citation_journal_title=Internat. J. Math.; citation_title=Schematic Harder-Narasimhan stratification; citation_author=N Nitsure; citation_volume=22; citation_issue=10; citation_publication_date=2011; citation_pages=1365-1373; citation_doi=10.1142/S0129167X11007264; citation_id=CR28

Porta, M., Sala, F.: Two-dimensional categorified Hall algebras (2019).

arXiv:1903.07253

Rapčák, M., Soibelman, Y., Yang, Y., Zhao, G.: Cohomological Hall algebras, vertex algebras and instantons. Comm. Math. Phys. 376(3), 1803–1873 (2020).

arXiv:1810.10402

Ren, J., Soibelman, Y.: Cohomological Hall algebras, semicanonical bases and Donaldson–Thomas invariants for $2$-dimensional Calabi–Yau categories (with an appendix by Ben Davison). In: Auroux, D. et al. (eds.) Algebra, Geometry, and Physics in the 21st Century. Progress in Mathematics, vol. 324. Birkhäuser, Cham (2017).

arXiv:1508.06068

Sala, F., Schiffmann, O.: Cohomological Hall algebra of Higgs sheaves on a curve. Algebr. Geom. 7(3), 346–376 (2020).

arXiv:1801.03482

citation_journal_title=Publ. Math. Inst. Hautes Études Sci.; citation_title=Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on

; citation_author=O Schiffmann, E Vasserot; citation_volume=118; citation_publication_date=2013; citation_pages=213-342; citation_doi=10.1007/s10240-013-0052-3; citation_id=CR33

Schiffmann, O., Vasserot, E.: On cohomological Hall algebras of quivers: generators. J. Reine Angew. Math. 760, 59–132 (2020).

arXiv:1705.07488

Schiffmann, O., Vasserot, E.: On cohomological Hall algebras of quivers: Yangians (2017).

arXiv:1705.07491

Soibelman, Y.: Remarks on cohomological Hall algebras and their representations. In: Ballmann, W. et al. (eds.) Arbeitstagung Bonn 2013. Progress in Mathematics, vol. 319, pp. 355–385. Birkhäuser, Cham (2016).

arXiv:1404.1606

Tanaka, Y., Thomas, R.P.: Vafa–Witten invariants for projective surfaces I: stable case. J. Algebraic Geom. 29(4), 603–668 (2020).

arXiv:1702.08487

citation_journal_title=Proc. London Math. Soc.; citation_title=The cohomological Hall algebra of a preprojective algebra; citation_author=Y Yang, G Zhao; citation_volume=116; citation_issue=5; citation_publication_date=2018; citation_pages=1029-1074; citation_doi=10.1112/plms.12111; citation_id=CR38

Zhao, Y.: On the

$$K$$

-theoretic Hall algebra of a surface. IMRN, rnaa123 (2020).

arXiv:1901.00831