Tomoyuki Arakawa


E-MAIL: arakawa at

Research Interest: Representation Theory, Vertex Algebras

Last Update: 21-Sep-2017

Curriculum Vitae (pdf)

I am currently visiting MIT until Janurary 31, 2018.

RIMS Representation Theory Seminar

RIMS project 2018: Vertex operator algebras and symmetry

Past Conferences


  1. Associated Varieties and Higgs Branches (A Survey), submitted to the proceeding for AMS Special Session on Vertex Algebras and Geometry.
  2. (with C. Jiang) Coset Vertex Operator Algebras and W-Algebras, arXiv:1701.06880 [math.RT], to appear in Special issue on Representation Theory in Sci. Schina. Math.
  3. (with C.-H. Lam and H. Yamada) Parafermion vertex operator algebras and W-algebras, arXiv:1701.06229 [math.RT].
  4. (with J. van Ekeren) Modularity of relatively rational vertex algebras and fusion rules of regular affine W-algebras, arXiv:1612.09100[math.RT].
  5. (with A. Premet) Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras, arXiv:1611.00852 [math.RT], to appear in the special issue of Proceedings of Moscow Math. Society dedicated to Vinberg's 80th birthday.
  6. (with T. Creutzig, K. Kawasetsu and A. Linshaw) Orbifolds and cosets of minimal $\mathcal{W}$-algebras, Comm. Math. Phys., October 2017, Volume 355, Issue 1, pp 339–372.
  7. (with H. Yamada and H. Yamauchi) Vertex operator algebras associated with Z/kZ-codes, In: Dobrev V. (eds) Lie Theory and Its Applications in Physics. LT 2015. Springer Proceedings in Mathematics & Statistics, vol 191. Springer, Singapore.
  8. (with K. Kawasetsu) Quasi-lisse vertex algebras and modular linear differential equations, arXiv:1610.05865 [math.QA], to appear in Kostant Memorial Volume, Birkhauser.
  9. (with A. Moreau) On the irreducibility of associated varieties of W-algebras, in the special issue of J. Algebra in Honor of Efim Zelmanov on occasion of his 60th anniversary, published online.
  10. (with V. Futorny, L.-E. Ramirez) Weight representations of admissible affine vertex algebras, Comm. Math. Phys. 353 (2017), no.3, 1151-1178.
  11. Introduction to W-algebras and their representation theory, arXiv:1605.00138 [math.RT], in Perspectives in Lie Theory, Springer INdAM Series 19.
  12. (with A. Moreau) Sheets and associated varieties of affine vertex algebras, Adv. Math, Volume 320, 7 November 2017, Pages 157–209.
  13. (with T. Creutzig and A. Linshaw) Cosets of Bershadsky-Polyakov algebras and rational $\mathcal{W}$-algebras of type $A$, Sel. Math. New Ser, October 2017, Volume 23, Issue 4, pp 2369–2395.
  14. (with A. Moreau) Joseph ideals and lisse minimal W-algebras, J. Inst. Math. Jussieu, published online.
  15. (with W. Wang) Modular affine vertex algebras and baby Wakimoto modules,Proc. Symp. Pure Math.,Volume: 92 (2016),14-29
  16. (with A. Molev) Explicit generators in rectangular affine W-algebras of type A, Lett. Math. Phys.107(1), 47-59, 2017.
  17. Rationality of W-algebras: principal nilpotent cases, Ann. Math. 182 (2015), 565-604.
  18. Rationality of admissible affine vertex algebras in the category O, Duke Math. J, Volume 165, Number 1 (2016), 67-93, errata.
  19. Two-sided BGG resolutions of admissible representations, Represent. Theory 18 (2014), 183-222.
  20. (with C.-H. Lam and H. Yamada) Zhu's algebra, C_2-algebra and C_2-cofiniteness of parafermion vertex operator algebras, Adv. Math., vol.264 (2014), 261--295.
  21. (with T. Kuwabara and F. Malikov) Localization of affine W-algebras, Comm. Math. Phys, April 2015, Volume 335, Issue 1, pp 143-182.
  22. W-algebras at the critical level, Contemp. Math., 565, 1--14, 2012.
  23. Rationality of Bershadsky-Polyakov vertex algebras, Comm. Math. Phys., October 2013, Volume 323, Issue 2, pp 627-633.
  24. Associated varieties of modules over Kac-Moody algebras and $C_2$-cofiniteness of W-algebras, Int. Math. Res. Notices (2015) Vol. 2015 11605--11666.
  25. A remark on the $C_2$-cofiniteness condition on vertex algebras, Math. Z. vol. 270, no. 1-2, 559-575, 2012.
  26. (with F. Malikov) A vertex algebra attached to the flag manifold and Lie algebra cohomology, AIP Conf. Proc. 1243, pp. 151-164, 2009, arXiv:0911.0922 [math.AG].
  27. (with P. Fiebig) The linkage principle for restricted critical level representations of affine Kac-Moody algebras, Compos. Math., 148, 1787--1810, 2012.
  28. (with F. Malikov) A chiral Borel-Weil-Bott theorem, Adv. Math., 229 (2012) 2908-2949.
  29. (with P. Fiebig) On the restricted Verma modules at the critical level, Trans. Amer. Math. Soc. 364 (2012), 4683-4712.
  30. (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.
  31. Representation theory of W-algebras, II, Adv. Stud. Pure Math. 61(2011), 51--90.
  32. Characters of representations of affine Kac-Moody Lie algebras at the critical level, arXiv:0706.1817v2 [math.QA].
  33. Representation Theory of W-Algebras, Invent. Math., Vol. 169 (2007), no. 2, 219--320.
  34. A New Proof of the Kac-Kazhdan Conjecture, Int. Math. Res. Not. 2006. Art. ID 27091, 5 pages.
  35. Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture, Duke Math. J., Vol. 130 (2005), No. 3, 435-478.
  36. Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction, Int. Math. Res. Not. 2004, no.15, 730--767.
  37. Drinfeld functor and finite-dimensional representations of Yangian, Comm. Math. Phys. 205 (1999), no. 1, 1--18.
  38. (with T. Suzuki) Duality between $sl_n(C)$ and the degenerate affine Hecke algebra, J. Algebra 209 (1998), no. 1, 288--304.
  39. (wih T. Suzuki and A. Tsuchiya) Degenerate double affine Hecke algebra and conformal field theory. Topological field theory, primitive forms and related topics (Kyoto, 1996), 1--34, Progr. Math., 160, Birkhauser, 1998.
  40. (with T. Nakanishi, K. Oshima and A. Tsuchiya) Spectral decomposition of path space in solvable lattice model. Comm. Math. Phys. 181 (1996), no. 1, 157--182.