Tomoyuki Arakawa


E-MAIL: arakawa at

Research Interest: Representation Theory, Vertex Algebras

Last Update: 15-Feb-2017

Curriculum Vitae (pdf)

I will give a graduate course at MIT for Spring Semester, 2016. The details will be here.

RIMS Representation Theory Seminar

Workshop on W-algebras, November 28 - December 2, 2016, University of Melbourne.

ESI conference on Geometry and Representation Theory, January 16-27, 2017, Vienna

Past Conferences


  1. (with C. Jiang) Coset Vertex Operator Algebras and W-Algebras, arXiv:1701.06880 [math.RT].
  2. (with C.-H. Lam and H. Yamada) Parafermion vertex operator algebras and W-algebras, arXiv:1701.06229 [math.RT].
  3. (with J. van Ekeren) Modularity of relatively rational vertex algebras and fusion rules of regular affine W-algebras, arXiv:1612.09100[math.RT].
  4. (with A. Premet) Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras, arXiv:1611.00852 [math.RT].
  5. (with T. Creutzig, K. Kawasetsu and A. Linshaw) Orbifolds and cosets of minimal $\mathcal{W}$-algebras, arXiv:1610.09348 [math.RT].
  6. (with H. Yamada and H. Yamauchi) Vertex operator algebras associated with Z/kZ-codes, Springer Proceedings in Mathematics & Statistics, Vol. 191, Pages 513-521.
  7. (with K. Kawasetsu) Quasi-lisse vertex algebras and modular linear differential equations, arXiv:1610.05865 [math.QA].
  8. (with A. Moreau) On the irreducibility of associated varieties of W-algebras, arXiv:1608.03142 [math.RT].
  9. (with V. Futorny, L.-E. Ramirez) Weight representations of admissible affine vertex algebras, arXiv:1605.07580 [math.RT], to appear in Comm. Math. Phys.
  10. Introduction to W-algebras and their representation theory, arXiv:1605.00138 [math.RT].
  11. (with A. Moreau) Sheets and associated varieties of affine vertex algebras, arXiv:1601.05906 [math.RT].
  12. (with T. Creutzig and A. Linshaw) Cosets of Bershadsky-Polyakov algebras and rational $\mathcal{W}$-algebras of type $A$, arXiv:1511.09143 [math.RT].
  13. (with A. Moreau) Joseph ideals and lisse minimal W-algebras, J. Inst. Math. Jussieu, published online.
  14. (with W. Wang) Modular affine vertex algebras and baby Wakimoto modules,Proc. Symp. Pure Math.,Volume: 92 (2016),14-29
  15. (with A. Molev) Explicit generators in rectangular affine W-algebras of type A, Lett. Math. Phys.107(1), 47-59, 2017.
  16. Rationality of W-algebras: principal nilpotent cases, Ann. Math. 182 (2015), 565-604.
  17. Rationality of admissible affine vertex algebras in the category O, Duke Math. J, Volume 165, Number 1 (2016), 67-93, errata.
  18. Two-sided BGG resolutions of admissible representations, Represent. Theory 18 (2014), 183-222.
  19. (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.
  20. (with T. Kuwabara and F. Malikov) Localization of affine W-algebras, Comm. Math. Phys, April 2015, Volume 335, Issue 1, pp 143-182.
  21. W-algebras at the critical level, Contemp. Math., 565, 1--14, 2012.
  22. Rationality of Bershadsky-Polyakov vertex algebras, Comm. Math. Phys., October 2013, Volume 323, Issue 2, pp 627-633.
  23. Associated varieties of modules over Kac-Moody algebras and $C_2$-cofiniteness of W-algebras, Int. Math. Res. Notices (2015) Vol. 2015 11605--11666.
  24. A remark on the $C_2$-cofiniteness condition on vertex algebras, Math. Z. vol. 270, no. 1-2, 559-575, 2012.
  25. (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].
  26. (with P. Fiebig) The linkage principle for restricted critical level representations of affine Kac-Moody algebras, Compos. Math., 148, 1787--1810, 2012.
  27. (with F. Malikov) A chiral Borel-Weil-Bott theorem, Adv. Math., 229 (2012) 2908-2949.
  28. (with P. Fiebig) On the restricted Verma modules at the critical level, Trans. Amer. Math. Soc. 364 (2012), 4683-4712.
  29. (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.
  30. Representation theory of W-algebras, II, Adv. Stud. Pure Math. 61(2011), 51--90.
  31. Characters of representations of affine Kac-Moody Lie algebras at the critical level, arXiv:0706.1817v2 [math.QA].
  32. Representation Theory of W-Algebras, Invent. Math., Vol. 169 (2007), no. 2, 219--320.
  33. A New Proof of the Kac-Kazhdan Conjecture, Int. Math. Res. Not. 2006. Art. ID 27091, 5 pages.
  34. Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture, Duke Math. J., Vol. 130 (2005), No. 3, 435-478.
  35. Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction, Int. Math. Res. Not. 2004, no.15, 730--767.
  36. Drinfeld functor and finite-dimensional representations of Yangian, Comm. Math. Phys. 205 (1999), no. 1, 1--18.
  37. (with T. Suzuki) Duality between $sl_n(C)$ and the degenerate affine Hecke algebra, J. Algebra 209 (1998), no. 1, 288--304.
  38. (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.
  39. (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.