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Urod algebras and Translation of W-algebras

Arakawa, Tomoyuki Creutzig, Thomas Feigin, Boris 京都大学 DOI:10.1017/fms.2022.15

2022

概要

In this work, we introduce Urod algebras associated to simply laced Lie algebras as well as the concept of translation of W-algebras. Both results are achieved by showing that the quantum Hamiltonian reduction commutes with tensoring with integrable representations; that is, for V and L an affine vertex algebra and an integrable affine vertex algebra associated with g, we have the vertex algebra isomorphism H⁰[DS, f](V⊗L)≅H⁰[DS, f] ((V)⊗L, where in the left-hand-side the Drinfeld–Sokolov reduction is taken with respect to the diagonal action of ˆg on V⊗L. The proof is based on some new construction of automorphisms of vertex algebras, which may be of independent interest. As corollaries, we get fusion categories of modules of many exceptional W-algebras, and we can construct various corner vertex algebras. A major motivation for this work is that Urod algebras of type A provide a representation theoretic interpretation of the celebrated Nakajima–Yoshioka blowup equations for the moduli space of framed torsion free sheaves on ℂℙ² of an arbitrary rank.

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参考文献

(1)

[AM95] D. Adamović and A. Milas, ‘Vertex operator algebras associated to modular invariant representations for 𝐴1 ’,

Math. Res. Lett. 2(5) (1995), 563–575.

[AGT10] L. F. Alday, D. Gaiotto and Y. Tachikawa, ‘Liouville correlation functions from four-dimensional gauge theories‘,

Lett. Math. Phys. 91(2) (2010), 167–197.

[AFO18] M. Aganagic, E. Frenkel and A. Okounkov, ‘Quantum 𝑞-Langlands correspondence’, Trud. Mosk. Mat. Obshch.

79(1) (2018), 1–95.

[Ara04] T. Arakawa, ‘Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction’, Int. Math. Res. Not. 15

(2004), 730–767.

[Ara05] T. Arakawa, ‘Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture’, Duke

Math. J. 130(3) (2005), 435–478.

[Ara07] T. Arakawa, ‘Representation theory of 𝑊 -algebras’, Invent. Math. 169(2) (2007), 219–320.

[Ara11] T. Arakawa, ‘Representation theory of 𝑊 -algebras, II’, In Exploring New Structures and Natural Constructions in

Mathematical Physics, Adv. Stud. Pure Math., Vol. 61 (Math. Soc. Japan, Tokyo, 2011), 51–90.

[Ara12] T. Arakawa, ‘A remark on the 𝐶2 cofiniteness condition on vertex algebras’, Math. Z. 270(1–2) (2012), 559–575.

[Ara14] T. Arakawa, ‘Two-sided BGG resolution of admissible representations’, Represent. Theory 18(3) (2014), 183–222.

[Ara15a] T. Arakawa, ‘Associated varieties of modules over Kac–Moody algebras and 𝐶2 -cofiniteness of W-algebras. Int.

Math. Res. Not. 2015 (2015), 11605–11666.

[Ara15b] T. Arakawa, ‘Rationality of W-algebras: Principal nilpotent cases’, Ann. Math. 182(2) (2015), 565–694.

[Ara16a] T. Arakawa, ‘Rationality of admissible affine vertex algebras in the category O”, Duke Math. J. 165(1) (2016), 67–93.

[Ara17] T. Arakawa, Introduction to W-Algebras and Their Representation Theory, Springer INdAM Series, Vol. 19 (Springer,

2017).

[Ara18] T. Arakawa, ‘Chiral algebras of class S and Moore–Tachikawa symplectic varieties’, Preprint, arXiv: 1811.01577.

[ACK] T. Arakawa, T. Creutzig and K. Kawasetsu, ‘Lisse principal W-algebras,’ In preparation.

[ACL17] T. Arakawa, T. Creutzig and A. R. Linshaw, ‘Cosets of Bershadsky–Polyakov algebras and rational W-algebras of

type A’, Selecta Mathematica 23(4) (2017), 2369–2395.

[ACL19] T. Arakawa, T. Creutzig and A. R. Linshaw, ‘A W-algebras as coset vertex algebras’, Inventiones mathematicae 218

(2019), 145–195.

[AF19] T. Arakawa and E. Frenkel, ‘Quantum Langlands duality of representations of 𝑊 -algebras’, Compos. Math. 155(12)

(2019), 2235–2262.

[AvE19] T. Arakawa and J. van Ekeren, ‘Modularity of relatively rational vertex algebras and fusion rules of regular affine

W-algebras’, Comm. Math. Phys. 370(1) (2019), 205–247.

[AvE] T. Arakawa and J. van Ekeren, ‘Rationality and fusion rules of exceptional W-algebras’, In J. Eur. Math. Soc. (JEMS),

to appear, arXiv: 1905.11473.

[AK18] T. Arakawa and K. Kawasetsu, ‘Quasi-lisse vertex algebras and modular linear differential equations’, In Lie Groups,

Geometry, and Representation Theory, Progr. Math., Vol. 326 (Birkhäuser/Springer, Cham, 2018), 41–57.

[AKM15] T. Arakawa, T. Kuwabara and F. Malikov, ‘Localization of Affine W-Algebras’, Comm. Math. Phys. 335(1) (2015),

143–182.

[AM] T. Arakawa and A. Moreau, ‘Arc spaces and chiral symplectic cores’, Publ. Res. Inst. Math. 57(3) (2021), 795–829.

[AG02] S. Arkhipov and D. Gaitsgory, ‘Differential operators on the loop group via chiral algebras’, Int. Math. Res. Not. (4)

(2002), (165–210.

[BD04] A. Beilinson and V. Drinfeld, Chiral Algebras, American Mathematical Society Colloquium Publications, Vol. 51

(American Mathematical Society, Providence, RI, 2004).

[BFL16] M. Bershtein, B. Feigin and A. Litvinov, ‘Coupling of two conformal field theories and Nakajima–Yoshioka blow-up

equations’, Lett. Math. Phys. 106(1) (2016), 29–56.

[Cre19] T. Creutzig, ‘Fusion categories for affine vertex algebras at admissible levels’, Selecta Mathematica 25(2) (2019), 27.

[CG17] T. Creutzig and D. Gaiotto, ‘Vertex Algebras for S-duality’, Commun. Math. Phys. 379, (2020), 785–845.

[CGL18] T. Creutzig, D. Gaiotto and A. R. Linshaw, ‘S-duality for the large 𝑁 = 4superconformal algebra’, Commun. Math.

Phys. 374(3) (2020), 1787-1808.

https://doi.org/10.1017/fms.2022.15 Published online by Cambridge University Press

A Self-archived copy in

Kyoto University Research Information Repository

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

30

Tomoyuki Arakawa et al.

[CGN] T. Creutzig, N. Genra and S. Nakatsuka, ‘Duality of subregular W-algebras and principal W-superalgebras’, Adv.

Math. 383(4) (2021), 107685.

[CHY18] T. Creutzig, Y.-Z. Huang and J. Yang, ‘Braided tensor categories of admissible modules for affine Lie algebras’,

Comm. Math. Phys. 362(3) (2018), 827–854.

[CJORY20] T. Creutzig, C. Jiang, F. O. Hunziker, D. Ridout and J. Yang, ‘Tensor categories arising from the Virasoro algebra’,

Adv. Math. 380(26) (2021), 107601

[CKM17] T. Creutzig, S. Kanade and R. McRae, ‘Tensor categories for vertex operator superalgebra extensions’, Mem. Am.

Math. Soc. Preprint, arXiv: 1705.05017.

[CKM19] T. Creutzig, S. Kanade and R. McRae, ‘Glueing vertex algebras’, Adv. Math. 396 (2022), 108174.

[CL20] T. Creutzig and A. R. Linshaw, ‘Trialities of W-algebras’, Cambridge Journal of Mathematics 10(1) (2022),

69–194.

[CL21] T. Creutzig and A. R. Linshaw, ‘Trialities of orthosymplectic W-algebras’, Preprint, arXiv:2102.10224v2 [math.RT].

[CMY20] T. Creutzig, R. McRae and J. Yang, ‘Direct limit completions of vertex tensor categories’, Commun. Contemp. Math.

published online.

[CY20] T. Creutzig and J. Yang, ‘Tensor categories of affine Lie algebras beyond admissible level’, Math. Ann. (3–4) (2021),

1991–2040.

[DSK06] A. De Sole and V. G. Kac, ‘Finite vs affine 𝑊 -algebras’, Japan. J. Math. 1(1) (2006), 137–261.

[FBZ04] E. Frenkel and D. Ben-Zvi, Vertex Algebras and Algebraic Curves, 2nd ed., Mathematical Surveys and Monographs,

Vol. 88 (American Mathematical Society, Providence, RI, 2004).

[Fe˘ı84] B. Fe˘ıgin, ‘Semi-infinite homology of Lie, Kac–Moody and Virasoro algebras’, Uspekhi Mat. Nauk 39(2) (1984),

195–196.

[FF90a] B. Feigin and E. Frenkel, ‘Quantization of the Drinfel d-Sokolov reduction’, Phys. Lett. B 246(1–2) (1990), 75–81.

[FF90b] B. L. Fe˘ıgin and E. V. Frenkel, ‘Affine Kac–Moody algebras and semi-infinite flag manifolds’, Comm. Math. Phys.

128(1) (1990), 161–189.

[FF91] B. Feigin and E. Frenkel, ‘Duality in W -algebras’, International Mathematics Research Notices 1991(6) (1991),

75–82, 03.

[FG18] B. Feigin and S. Gukov, ‘VOA[𝑀4 ]’, J. Math. Phys. 61(1) (2020), 012302.

[Fre92] E. Frenkel, ‘Determinant formulas for the free field representations of the Virasoro and Kac-Moody algebras’, Phys.

Lett. B 286(1–2) (1992), 71–77.

[Fre05] E. Frenkel, ‘Wakimoto modules, opers and the center at the critical level’, Adv. Math. 195(2) (2005), 297–404.

[FG10] E. Frenkel and D. Gaitsgory, ‘Weyl modules and opers without monodromy’, In Arithmetic and Geometry around

Quantization, Progr. Math., Vol. 279 (Birkhäuser Boston Inc., Boston, MA, 2010), 101–121.

[FKW92] E. Frenkel, V. Kac and Minoru Wakimoto, ‘Characters and fusion rules for 𝑊 -algebras via quantized Drinfel

d-Sokolov reduction’, Comm. Math. Phys., 147(2) (1992), 295–328.

[FS06] I. B. Frenkel and K. Styrkas, ‘Modified regular representations of affine and Virasoro algebras, VOA structure and

semi-infinite cohomology’, Adv. Math. 206(1) (2006), 57–111.

[FZ92] I. B. Frenkel and Y. Zhu, ‘Vertex operator algebras associated to representations of affine and Virasoro algebras’,

Duke Math. J. 66(1) (1992), 123–168.

[Goo11] S. M. Goodwin, ‘Translation for finite 𝑊 -algebras’, Represent. Theory 15 (2011), 307–346.

[Hua08] Y.-Z. Huang, ‘Rigidity and modularity of vertex tensor categories’, Commun. Contemp. Math. 10(suppl. 1) (2008),

871–911.

[Hua09] Y.-Z. Huang, ‘Cofiniteness conditions, projective covers and the logarithmic tensor product theory’, Journal of Pure

and Applied Algebra 213(4) (2009), 458–475.

[HL94] Y.-Z. Huang and J. Lepowsky, ‘Tensor products of modules for a vertex operator algebra and vertex tensor categories’,

In Lie Theory and Geometry, Progr. Math., Vol. 123 (Birkhäuser Boston, Boston, MA, 1994), 349–383.

[HL95] Y.-Z. Huang and J. Lepowsky, ‘A theory of tensor products for module categories for a vertex operator algebra. I, II,

Selecta Math. (N.S.) 1(4) (1995), 699–756, 757–786.

[HLZ14] Yi-Zhi Huang, J. Lepowsky and L. Zhang, ‘Logarithmic tensor category theory for generalized modules for a

conformal vertex algebra, I: Introduction and strongly graded algebras and their generalized modules’, In Conformal

Field Theories and Tensor Categories, Math. Lect. Peking Univ., (Springer, Heidelberg, 2014), 169–248.

[KL1] D. Kazhdan and G. Lusztig, ‘Tensor structure arising from affine Lie algebras I’, J. Amer. Math. Soc. 6 (1993),

905–947.

[KL2] D. Kazhdan and G. Lusztig, ‘Tensor structure arising from affine Lie algebras II’, J. Amer. Math. Soc. 6 (1993),

949–1011.

[KL3] D. Kazhdan and G. Lusztig, ‘Tensor structure arising from affine Lie algebras III’, J. Amer. Math. Soc. 7 (1994),

335–381.

[KL4] D. Kazhdan and G. Lusztig, ‘Tensor structure arising from affine Lie algebras IV’, J. Amer. Math. Soc. 7 (1994),

383–453.

[KRW03] V. Kac, S.-S. Roan and M. Wakimoto, ‘Quantum reduction for affine superalgebras’, Comm. Math. Phys. 241(2–3)

(2003), 307–342.

https://doi.org/10.1017/fms.2022.15 Published online by Cambridge University Press

A Self-archived copy in

Kyoto University Research Information Repository

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

Forum of Mathematics, Sigma

31

[KW89] V. Kac and M. Wakimoto, ‘Classification of modular invariant representations of affine algebras’, In InfiniteDimensional Lie Algebras and Groups (Luminy–Marseille, 1988), Adv. Ser. Math. Phys., Vol. 7 (World Sci. Publ.

Teaneck, NJ, 1989), 138–177.

[KW94] V. G. Kac and M. Wakimoto, ‘Integrable highest weight modules over affine superalgebras and number theory’, In

Lie Theory and Geometry, Progr. Math., Vol. 123 (Birkhäuser Boston, Boston, MA, 1994), 415–456.

[KW01] V. G. Kac and M. Wakimoto, ‘Integrable highest weight modules over affine superalgebras and Appell’s function’,

Commun. Math. Phys. 215 (2001) 631-682.

[KW04] V. G. Kac and M. Wakimoto, ‘Quantum reduction and representation theory of superconformal algebras’, Adv. Math.

185(2) (2004), 400–458.

[KW05] V. G. Kac and M. Wakimoto, ‘Corrigendum to: “Quantum reduction and representation theory of superconformal

algebras’, Adv. Math. 185(2) (2004), 400–458; mr2060475], Adv. Math. 193(2) (2005), 453–455.

[KW08] V. G. Kac and M. Wakimoto, ‘On rationality of 𝑊 -algebras’, Transform. Groups 13(3–4) (2008), 671–713.

ˆ 2 conformal

[KO02] A. Kirillov and V. Ostrik, ‘On a q-analogue of the Mckay correspondence and the ADE classification of sl

field theories’, Advances in Mathematics 171(2) (2002), 183 – 227.

[LL04] J. Lepowsky and H. Li, Introduction to Vertex Operator Algebras and Their Representations, Progress in Mathematics, Vol. 227 (Birkhäuser Boston, Inc., Boston, MA, 2004).

[Mü03] M. Müger, ‘From subfactors to categories and topology. II. The quantum double of tensor categories and subfactors’,

J. Pure Appl. Algebra 180(1–2) (2003), 159–219.

[MSV99] F. Malikov, V. Schechtman and A. Vaintrob, ‘Chiral de Rham complex’, Comm. Math. Phys. 204(2) (1999), 439–473.

[NY05] H. Nakajima and K. Yoshioka, ‘Instanton counting on blowup. I. 4-dimensional pure gauge theory’, Inventiones

mathematicae 162(2) (2005), 313–355.

[Pre02] A. Premet, ‘Special transverse slices and their enveloping algebras’, Adv. Math. 170(1) (2002), 1–55, With an

appendix by Serge Skryabin.

[SV13] O. Schiffmann and E. Vasserot, ‘Cherednik algebras, W-algebras and the equivariant cohomology of the moduli

space of instantons on 𝐴2 ’, Publications mathématiques de l’IHÉS 118(1) (2013), 213–342.

[Zhu08] M. Zhu, ‘Vertex operator algebras associated to modified regular representations of affine Lie algebras’, Adv. Math.

219(5) (2008), 1513–1547.

https://doi.org/10.1017/fms.2022.15 Published online by Cambridge University Press

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