Professor

Research Institute for Mathematical Sciences, Kyoto University

E-MAIL: arakawa at kurims.kyoto-u.ac.jp

Research Interest: Representation Theory, Vertex Algebras

Last Update： 04-Apr-2024

Some videos of my talks

- "4d/2d duality and representation therory" (1,2,3,4) at HSE, Moscow, April, 2019.
- ICM 2018 talk "Representation theory of W-algebras and Higgs branch conjecture".

RIMS Representation Theory Seminar

Thematic Program on Vertex and Chiral Algebras, February - May 2022, IMPA, Rio de Janeiro, Brazil.

Vertex Algebras and Representation Theory, 6-10 June, 2022, CIRM, France.

Recent preprints

- (with V. Futorny and L. Krizka) Generalized Grothendieck's simultaneous resolution and associated varieties of simple affine vertex algebras, arXiv:2404.02365[math.RT].
- (with X. Dai, J. Fasquel, Bohan Li and A. Moreau) On a series of simple affine VOAs at non-admissible level arising from rank one 4D SCFTs, arXiv:2403.04472 [math.RT].
- (with T. Creutzig and K. Kawasetsu) Weight representations of affine Kac-Moody algebras and small quantum groups, aarXiv:2311.10233[math.RT].
- (with T. Kuwabara and S. Möller) Hilbert Schemes of Points in the Plane and Quasi-Lisse Vertex Algebras with N=4 Symmetry, arXiv:2309.17308 [math.RT].
- (with L. Topley and J. J. Villarreal) The centre of the modular affine vertex algebra at the critical level, arXiv:2305.17765 [math.QA].
- (with J. van Ekeren and A. Moreau) Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras,arXiv:2102.13462 [math.RT].
- (with J. van Ekeren and A. Moreau) On the nilpotent orbits arising from admissible affine vertex algebras, arXiv:2010.08429 [math.RT],
*Proc. Lond. Math. Soc., published online.* - (with T. Creutzig and B. Feigin) Urod algebras and Translation of W-algebras, arXiv:2010.02427 [math.RT],
*Forum of Mathematics, Sigma, Volume 10, 2022, e33.* - (with K. Kawasetsu and J. Sebag) A question of Joseph Ritt from the point of view of vertex algebras, arXiv:2009.04615 [math.QA],
*J. Algebra, Volume 588, 15 December 2021, Pages 118-12*. - (with C. Jiang and A. Moreau) Simplicity of vacuum modules and associated varieties, arXiv:2003.12997 [math.RT],
*J. Éc. polytech. Math, Tome 8 (2021), pp. 169-191.* - (with H. Yamada and H. Yamauchi) $\mathbb{Z}_k$-code vertex operator algebras, arXiv:1907.10216 [math.RT],
*J. Math. Soc. Japan, Volume 73, Number 1 (2021), 185-209.* - (with J. van Ekeren) Rationality and Fusion Rules of Exceptional W-Algebras, arXiv:1905.11473 [math.RT],
*J. Eur. Math. Soc. (JEMS) (online first)*. - Chiral algebras of class $\mathcal{S}$ and Moore-Tachikawa symplectic varieties, arXiv:1811.01577 [math.RT].

Selected papers

- (with E. Frenkel) Quantum Langlands duality of representations of W-algebras,
*Compos. Math.*Volume 155, Issue 12, December 2019, 2235-2262. - (with T. Creutzig and A. Linshaw) W-algebras as coset vertex algebras,
*Invent. Math.,*October 2019, Volume 218, Issue 1, pp 145–195. - (with K. Kawasetsu) Quasi-lisse vertex algebras and modular linear differential equations, In: 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. - (with A. Moreau) Joseph ideals and lisse minimal W-algebras,
*J. Inst. Math. Jussieu*, 17 (2018), no. 2, 397–417. - (with A. Premet) Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras
*, Trans. Moscow Math. Soc.***2017**, 217-234. - Rationality of W-algebras: principal nilpotent cases,
*Ann. Math.*182 (2015), 565-604. - Rationality of admissible affine vertex algebras in the category O,
*Duke Math. J*, Volume 165, Number 1 (2016), 67-93, errata. - Associated varieties of modules over Kac-Moody algebras and $C_2$-cofiniteness of W-algebras,
*Int. Math. Res. Notices*(2015) Vol. 2015 11605--11666*.* - A remark on the $C_2$-cofiniteness condition on vertex algebras,
*Math. Z*. vol. 270, no. 1-2, 559-575, 2012. - (with F. Malikov) A chiral Borel-Weil-Bott theorem,
*Adv. Math.*, 229 (2012) 2908-2949. - (with P. Fiebig) The linkage principle for restricted critical level representations of affine Kac-Moody algebras,
*Compos. Math.,*148, 1787--1810, 2012. - (with D. Chebotarov and F. Malikov) Algebras of twisted chiral differential operators and affine localization of $g$-modules
*, Sel. Math. New Ser.*, vol.17, no. 1, 1-46, 2011. - Representation Theory of W-Algebras,
*Invent. Math.*, Vol. 169 (2007), no. 2, 219--320. - Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture,
*Duke Math. J.*, Vol. 130 (2005), No. 3, 435-478. - (with T. Suzuki) Duality between $sl_n(C)$ and the degenerate affine Hecke algebra,
*J. Algebra*209 (1998), no. 1, 288--304.

Here is the complete list of publications.

Servey articles and lecture notes

- Representation theory of W-algebras and Higgs branch conjecture,
*Proc. Int. Cong. of Math. 2018 Rio de Janeiro*, Vol. 1 (1261-1278). - Associated Varieties and Higgs Branches (A Survey),
*Contemp. Math.*711(2018), 37-44. - Introduction to W-algebras and their representation theory, In: Callegaro F., Carnovale G., Caselli F., De Concini C., De Sole A. (eds)
*Perspectives in Lie Theory. Springer INdAM Series*, vol 19. Springer.