荒川 知幸

English

 

京都大学数理解析研究所 教授

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

専門分野: 表現論,頂点代数

最終更新日: 2018年9月18日


研究室の紹介


過去の講義


RIMS 表現論セミナー

Algebraic Lie Thery and Rpresentation Theory 2018

RIMS project 2018:頂点作用素代数と対称性

・RIMS Gasshuku-style Seminar "Vertex Operator Algebras and Conformal Field Theory" (July 2 - 6, 2018)

・RIMS Workshop "Vertex Operator Algebras and Symmetries" (July 9 - 13, 2018)

過去の研究集会


論文

  1. (with E. Frenkel) Quantum Langlands duality of representations of W-algebras, arXiv:1807.01536 [math.QA].
  2. (with A. Linshaw) Singular support of a vertex algebra and the arc space of its associated scheme, arXiv:1804.01287 [math.RT], to appear in a special volume of Progress in Mathematics series in honour of 75's birthday of Antony Joseph.
  3. (with A. Moreau) Arc spaces and chiral symplectic cores, arXiv:1802.06533 [math.RT].
  4. (with T. Creutzig and A. Linshaw) W-algebras as coset vertex algebras, arXiv:1801.03822 [math.QA].
  5. Representation theory of W-algebras and Higgs branch conjecture, submitted to the Proceedings of the ICM 2018. 
  6. Associated Varieties and Higgs Branches (A Survey), Contemp. Math. 711(2018), 37-44.
  7. (with C. Jiang) Coset Vertex Operator Algebras and W-Algebras, Sci. China Math. 61 (2018), no. 2, 191–206. 17B69.
  8. (with C.-H. Lam and H. Yamada) Parafermion vertex operator algebras and W-algebras, arXiv:1701.06229 [math.RT], to appear in Trans. Amer. Math. Soc.
  9. (with J. van Ekeren) Modularity of relatively rational vertex algebras and fusion rules of regular affine W-algebras, arXiv:1612.09100[math.RT].
  10. (with A. Premet) Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras, Trans. Moscow Math. Soc. 2017, 217-234. 
  11. (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.
  12. (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.
  13. (with K. Kawasetsu) Quasi-lisse vertex algebras and modular linear differential equations, arXiv:1610.05865 [math.QA], to appear in Kostant Memorial Volume, Birkhauser.
  14. (with A. Moreau) On the irreducibility of associated varieties of W-algebras, J. Alg. 500, 15 April 2018, Pages 542-568.
  15. (with V. Futorny, L.-E. Ramirez) Weight representations of admissible affine vertex algebras, Comm. Math. Phys. 353 (2017), no.3, 1151-1178.
  16. 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.
  17. (with A. Moreau) Sheets and associated varieties of affine vertex algebras, Adv. Math, Volume 320, 7 November 2017, Pages 157–209.
  18. (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.
  19. (with A. Moreau) Joseph ideals and lisse minimal W-algebras, J. Inst. Math. Jussieu, 17 (2018), no. 2, 397–417. 
  20. (with W. Wang) Modular affine vertex algebras and baby Wakimoto modules, Proc. Symp. Pure Math., Volume: 92 (2016),14-29.
  21. (with A. Molev) Explicit generators in rectangular affine W-algebras of type A, Lett. Math. Phys. 107(1), 47-59, 2017.
  22. Rationality of W-algebras: principal nilpotent cases, Ann. Math. 182 (2015), 565-604.
  23. Rationality of admissible affine vertex algebras in the category O, Duke Math. J, Volume 165, Number 1 (2016), 67-93, errata.
  24. Two-sided BGG resolutions of admissible representations, Represent. Theory 18 (2014), 183-222.
  25. (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.
  26. (with T. Kuwabara and F. Malikov) Localization of affine W-algebras, Comm. Math. Phys, April 2015, Volume 335, Issue 1, pp 143-182.
  27. W-algebras at the critical level, Contemp. Math., 565, 1--14, 2012.
  28. Rationality of Bershadsky-Polyakov vertex algebras, Comm. Math. Phys., October 2013, Volume 323, Issue 2, pp 627-633.
  29. Associated varieties of modules over Kac-Moody algebras and $C_2$-cofiniteness of W-algebras, Int. Math. Res. Notices (2015) Vol. 2015 11605--11666.
  30. A remark on the $C_2$-cofiniteness condition on vertex algebras, Math. Z. vol. 270, no. 1-2, 559-575, 2012.
  31. (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].
  32. (with P. Fiebig) The linkage principle for restricted critical level representations of affine Kac-Moody algebras, Compos. Math., 148, 1787--1810, 2012.
  33. (with F. Malikov) A chiral Borel-Weil-Bott theorem, Adv. Math., 229 (2012) 2908-2949.
  34. (with P. Fiebig) On the restricted Verma modules at the critical level, Trans. Amer. Math. Soc. 364 (2012), 4683-4712.
  35. (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.
  36. Representation theory of W-algebras, II, Adv. Stud. Pure Math. 61(2011), 51--90.
  37. Characters of representations of affine Kac-Moody Lie algebras at the critical level, arXiv:0706.1817v2 [math.QA].
  38. Representation Theory of W-Algebras, Invent. Math., Vol. 169 (2007), no. 2, 219--320.
  39. A New Proof of the Kac-Kazhdan Conjecture, Int. Math. Res. Not. 2006. Art. ID 27091, 5 pages.
  40. Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture, Duke Math. J., Vol. 130 (2005), No. 3, 435-478.
  41. Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction, Int. Math. Res. Not. 2004, no.15, 730--767.
  42. Drinfeld functor and finite-dimensional representations of Yangian, Comm. Math. Phys. 205 (1999), no. 1, 1--18.
  43. (with T. Suzuki) Duality between $sl_n(C)$ and the degenerate affine Hecke algebra, J. Algebra 209 (1998), no. 1, 288--304.
  44. (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.
  45. (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.

賞罰

  1. ICM2018招待講演 (スライド)
  2. 平成29年度日本数学会秋季賞 (受賞講演のスライド)
  3. 平成25年度代数学賞
  4. 平成20年度文部科学大臣表彰若手科学者賞
  5. 平成16年度日本数学会建部賢弘特別賞

京都大学数理解析研究所