Arc Spaces and Chiral Symplectic Cores

[AG]

Sergey Arkhipov and Dennis Gaitsgory. Differential operators on the loop group via

chiral algebras. Int. Math. Res. Not., (4):165–210, 2002.

[A1]

Tomoyuki Arakawa. A remark on the C2 cofiniteness condition on vertex algebras. Math.

Z., 270(1-2):559–575, 2012.

[A2]

Tomoyuki Arakawa. W-algebras at the critical level. Contemp. Math., 565:1–14, 2012.

[A3]

Tomoyuki Arakawa. Associated varieties of modules over Kac-Moody algebras and C2 cofiniteness of W-algebras. Int. Math. Res. Not., 2015:11605–11666, 2015.

[A4]

Tomoyuki Arakawa. Rationality of W-algebras: principal nilpotent cases. Ann. Math.,

182(2):565–694, 2015.

[A5]

Tomoyuki Arakawa. Associated varieties and higgs branches (a survey). To appear in

Contemp. Math.

[A6]

Tomoyuki Arakawa. Chiral algebras of class S and Moore-Tachikawa symplectic varieties, Tomoyuki Arakawa. arXiv:1811.01577 [math.RT].

[AK]

Tomoyuki Arakawa and Kazuya Kawasetsu. Quasi-lisse vertex algebras and modular

linear differential equations, V. G. Kac, V. L. Popov (eds.), Lie Groups, Geometry, and

Representation Theory, A Tribute to the Life and Work of Bertram Kostant, Progr.

Math., 326, Birkhauser, 2018.

[AKM]

Tomoyuki Arakawa, Toshiro Kuwabara, and Fyodor Malikov. Localization of Affine

W-Algebras. Comm. Math. Phys., 335(1):143–182, 2015.

[AM1]

Tomoyuki Arakawa and Anne Moreau. Joseph ideals and lisse minimal W-algebras. J.

Inst. Math. Jussieu, 17(2):397–417, 2018.

[AM2]

Tomoyuki Arakawa and Anne Moreau. Sheets and associated varieties of affine vertex

algebras. Adv. Math., 320:157–209, 2017.

[AM3]

Tomoyuki Arakawa and Anne Moreau. On the irreducibility of associated varieties of

W-algebras. The special issue of J. Algebra in Honor of Efim Zelmanov on occasion of

his 60th anniversary, 500:542–568, 2018.

[BLL+ ] Christopher Beem, Madalena Lemos, Pedro Liendo, Wolfger Peelaers, Leonardo Rastelli,

and Balt C. van Rees. Infinite chiral symmetry in four dimensions. Comm. Math. Phys.,

336(3):1359–1433, 2015.

[BPRvR] Christopher Beem, Wolfge Peelaers, Leonardo Rastelli, and Balt C. van Rees. Chiral

algebras of class S, J. High Energ. Phys. (2015) 2015: 20.

[BR]

Christopher Beem and Leonardo Rastelli. Vertex operator algebras, Higgs branches,

and modular differential equations. J. High Energ. Phys. (2018) 2018: 114.

[BD1]

Alexander A. Beilinson and Vladimir G. Drinfeld. Quantization of Hitchin’s fibration

and Langlands’ program. In Algebraic and geometric methods in mathematical physics

(Kaciveli, 1993), volume 19 of Math. Phys. Stud., pages 3–7. Kluwer Acad. Publ.,

Dordrecht, 1996.

[BD2]

Alexander Beilinson and Vladimir Drinfeld. Chiral algebras, volume 51 of American

Mathematical Society Colloquium Publications. American Mathematical Society, Providence, RI, 2004.

[BMR]

Federico Bonetti, Carlo Meneghelli and Leonardo Rastelli. VOAs labelled by complex

reflection groups and 4d SCFTs. arXiv:1810.03612 [hep-th].

A Self-archived copy in

Kyoto University Research Information Repository

https://repository.kulib.kyoto-u.ac.jp

26

[Bor]

[BG]

[BKN]

[CM]

[CN]

[CCG]

[Cre]

[Dix]

[EM]

[EF]

[FF1]

[FF2]

[Fre]

[FJLS]

[GG]

[Gin1]

[Gin2]

[GW]

[GMS1]

[GMS2]

[Ish1]

[Ish2]

[Kac]

[Kol]

[KRW]

[Kos]

[KS]

[LP]

TOMOYUKI ARAKAWA AND ANNE MOREAU

Richard E. Borcherds. Vertex algebras, Kac-Moody algebras, and the Monster. Proc.

Nat. Acad. Sci. U.S.A., 83(10):3068–3071, 1986.

Kenneth A. Brown and Iain Gordon. Poisson orders, symplectic reflection algebras and

representation theory. J. Reine Angew. Math., 559:193–216, 2003.

Matthew Buican, Zoltan Laczko and Takahiro Nishinaka. N = 2 S-duality revisited, J.

High Energ. Phys. 09 (2017) 087.

Jean-Yves Charbonnel and Anne Moreau. The symmetric invariants of centralizers and

Slodowy grading. Math. Z., 282(1-2):273–339, 2016.

Jaewang Choi and Takahiro Nishinaka On the chiral algebra of Argyres-Douglas theories

and S-duality, J. High Energ. Phys. 04 (2018) 004.

Kevin Costello, Thomas Creutzig and Davide Gaiotto, Higgs and Coulomb branches

from vertex operator algebras. arXiv:1811.03958 [hep-th].

Thomas Creutzig. Logarithmic W-algebras and Argyres-Douglas theories at higher rank,

J. High Energ. Phys. 11 (2018) 188.

Jacques Dixmier. Enveloping algebras, volume 11 of Graduate Studies in Mathematics.

American Mathematical Society, Providence, RI, 1996. Revised reprint of the 1977

translation.

Lawrence Ein and Mircea Mustat¸˘

a. Jet schemes and singularities. In Algebraic

geometry—Seattle 2005. Part 2, volume 80 of Proc. Sympos. Pure Math., pages 505–

546. Amer. Math. Soc., Providence, RI, 2009.

David Eisenbud and Edward Frenkel. Appendix to [Mus]. 2001.

Boris Feigin and Edward Frenkel. Quantization of the Drinfel′ d-Sokolov reduction. Phys.

Lett. B, 246(1-2):75–81, 1990.

Boris Feigin and Edward Frenkel. Affine Kac-Moody algebras at the critical level and

Gel′ fand-Diki˘ı algebras. In Infinite analysis, Part A, B (Kyoto, 1991), volume 16 of

Adv. Ser. Math. Phys., pages 197–215. World Sci. Publ., River Edge, NJ, 1992.

Edward Frenkel. Langlands correspondence for loop groups, volume 103 of Cambridge

Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2007.

Baohua Fu, Daniel Juteau, Paul Levy, and Eric Sommers. Generic singularities of nilpotent orbit closures. Adv. Math., 305:1–77, 2017.

Wee Liang Gan and Victor Ginzburg. Quantization of Slodowy slices. Int. Math. Res.

Not., (5):243–255, 2002.

Victor Ginzburg. On primitive ideals. Selecta Math. (N.S.), 9(3):379–407, 2003.

Victor Ginzburg. Harish-Chandra bimodules for quantized Slodowy slices. Represent.

Theory, 13:236–271, 2009.

Roe Goodman and Nolan R. Wallach. Symmetry, representations, and invariants, volume 255 of Graduate Texts in Mathematics. Springer, Dordrecht, 2009.

Vassily Gorbounov, Fyodor Malikov, and Vadim Schechtman. On chiral differential

operators over homogeneous spaces. Int. J. Math. Math. Sci., 26(2):83–106, 2001.

Vassily Gorbounov, Fyodor Malikov, and Vadim Schechtman. Gerbes of chiral differential operators. II. Vertex algebroids. Invent. Math., 155(3):605–680, 2004.

Shihoko Ishii. The arc space of a toric variety. Journal of Algebra, 278:666–683, 2004.

Shihoko Ishii. Geometric properties of jet schemes. Comm. Algebra, 39(5):1872–1882,

2011.

Victor Kac. Introduction to vertex algebras, poisson vertex algebras, and integrable

Hamiltonian PDE. In Caselli F. De Concini C. De Sole A. Callegaro F., Carnovale G.,

editor, Perspectives in Lie Theory, volume 19 of Springer INdAM Series 19, pages 3–72.

Springer, 2017.

Ellis R. Kolchin. Differential algebra and algebraic groups. Academic Press, New YorkLondon, 1973. Pure and Applied Mathematics, Vol. 54.

Victor Kac, Shi-Shyr Roan, and Minoru Wakimoto. Quantum reduction for affine superalgebras. Comm. Math. Phys., 241(2-3):307–342, 2003.

Bertram Kostant. On Whittaker vectors and representation theory. Invent. Math.,

48(2):101–184, 1978.

Bertram Kostant and Shlomo Sternberg. Symplectic reduction, BRS cohomology, and

infinite-dimensional Clifford algebras. Ann. Physics, 176(1):49–113, 1987.

Madalena Lemos and Wolfger Peelaers, Chiral Algebras for Trinion Theories, J. High

Energ. Phys. 02 (2015) 113.

A Self-archived copy in

Kyoto University Research Information Repository

https://repository.kulib.kyoto-u.ac.jp

ARC SPACES AND CHIRAL SYMPLECTIC CORES

[Li]

[MSV]

[Mus]

[Pre1]

[Pre2]

[RsT]

[SXY]

[Van]

[Zhu]

27

Haisheng Li. Abelianizing vertex algebras. Comm. Math. Phys., 259(2):391–411, 2005.

Fyodor Malikov, Vadim Schechtman, and Arkady Vaintrob. Chiral de Rham complex.

Comm. Math. Phys., 204(2):439–473, 1999.

Mircea Mustat¸˘

a. Jet schemes of locally complete intersection canonical singularities.

Invent. Math., 145(3):397–424, 2001. With an appendix by David Eisenbud and Edward

Frenkel.

Alexander Premet. Special transverse slices and their enveloping algebras. Adv. Math.,

170(1):1–55, 2002. With an appendix by Serge Skryabin.

Alexander Premet. Enveloping algebras of Slodowy slices and the Joseph ideal. J. Eur.

Math. Soc., 9(3):487–543, 2007.

Mustapha Ra¨ıs and Patrice Tauvel. Indice et polynˆ

omes invariants pour certaines

alg`

ebres de Lie. J. Reine Angew. Math., 425:123–140, 1992.

Jaewon Song, Dan Xie and Wenbin Yan. Vertex operator algebras of Argyres-Douglas

theories from M5-branes, J. High Energ. Phys. 12 (2017) 123.

Pol Vanhaecke. Integrable systems in the realm of algebraic geometry, volume 1638 of

Lecture Notes in Mathematics. Springer-Verlag, Berlin, second edition, 2001.

Yongchang Zhu. Modular invariance of characters of vertex operator algebras. J. Amer.

Math. Soc., 9(1):237–302, 1996.

1 Research

Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502

JAPAN

E-mail address: arakawa@kurims.kyoto-u.ac.jp

2 Laboratoire Paul Painlev´

e de Lille, 59655 Villeneuve d’Ascq Cedex,

e, Universit´

France

E-mail address: anne.moreau@univ-lille.fr

...