# Tomoyuki Arakawa

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： 08-Nov-2021

Curriculum Vitae (pdf)

Some videos of my talks

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.

Past Conferences

Recent preprints

1. (with J. van Ekeren and A. Moreau) Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras,arXiv:2102.13462 [math.RT].
2. (with J. van Ekeren and A. Moreau) On the nilpotent orbits arising from admissible affine vertex algebras, arXiv:2010.08429 [math.RT].
3. (with T. Creutzig and B. Feigin) Urod algebras and Translation of W-algebras, arXiv:2010.02427 [math.RT].
4. (with K. Kawasetsu and J. Sebag) A question of Joseph Ritt from the point of view of vertex algebras, arXiv:2009.04615 [math.QA], to appear in J. Algebra.
5. (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.
6. (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.
7. (with J. van Ekeren) Rationality and Fusion Rules of Exceptional W-Algebras, arXiv:1905.11473 [math.RT], to appear in J. Eur. Math. Soc. (JEMS).
8. Chiral algebras of class $\mathcal{S}$ and Moore-Tachikawa symplectic varieties, arXiv:1811.01577 [math.RT].

Selected papers

1. (with E. Frenkel) Quantum Langlands duality of representations of W-algebras, Compos. Math. Volume 155, Issue 12, December 2019, 2235-2262.
2. (with T. Creutzig and A. Linshaw) W-algebras as coset vertex algebras, Invent. Math., October 2019, Volume 218, Issue 1, pp 145–195.
3. (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 TheoryA Tribute to the Life and Work of Bertram Kostant, Progr. Math., 326, Birkhauser, 2018.
4. (with A. Moreau) Joseph ideals and lisse minimal W-algebras, J. Inst. Math. Jussieu, 17 (2018), no. 2, 397–417.
5. (with A. Premet) Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras, Trans. Moscow Math. Soc. 2017, 217-234.
6. Rationality of W-algebras: principal nilpotent cases, Ann. Math. 182 (2015), 565-604.
7. Rationality of admissible affine vertex algebras in the category O, Duke Math. J, Volume 165, Number 1 (2016), 67-93, errata.
8. Associated varieties of modules over Kac-Moody algebras and $C_2$-cofiniteness of W-algebras, Int. Math. Res. Notices (2015) Vol. 2015 11605--11666.
9. A remark on the $C_2$-cofiniteness condition on vertex algebras, Math. Z. vol. 270, no. 1-2, 559-575, 2012.
10. (with F. Malikov) A chiral Borel-Weil-Bott theorem, Adv. Math., 229 (2012) 2908-2949.
11. (with P. Fiebig) The linkage principle for restricted critical level representations of affine Kac-Moody algebras, Compos. Math., 148, 1787--1810, 2012.
12. (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.
13. Representation Theory of W-Algebras, Invent. Math., Vol. 169 (2007), no. 2, 219--320.
14. Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture, Duke Math. J., Vol. 130 (2005), No. 3, 435-478.
15. (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

1. Representation theory of W-algebras and Higgs branch conjecture, Proc. Int. Cong. of Math. 2018 Rio de Janeiro, Vol. 1 (1261-1278).
2. Associated Varieties and Higgs Branches (A Survey), Contemp. Math. 711(2018), 37-44.
3. 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.

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