荒川 知幸

English

 

京都大学数理解析研究所 准教授

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: 2016年6月29日


研究室の紹介


2016年春学期: MITで大学院生向けの講義をします。内容はこちら

過去の講義


RIMS 表現論セミナー

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

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

過去の研究集会


論文

  1. (with V. Futorny, L.-E. Ramirez) Weight representations of admissible affine vertex algebras, arXiv:1605.07580 [math.RT].
  2. Introduction to W-algebras and their representation theory, arXiv:1605.00138 [math.RT].
  3. (with A. Moreau) Sheets and associated varieties of affine vertex algebras, arXiv:1601.05906 [math.RT].
  4. (with T. Creutzig and A. Linshaw) Cosets of Bershadsky-Polyakov algebras and rational $\mathcal{W}$-algebras of type $A$, arXiv:1511.09143 [math.RT].
  5. (with A. Moreau) Joseph ideals and lisse minimal W-algebras, J. Inst. Math. Jussieu, published online.
  6. (with W. Wang) Modular affine vertex algebras and baby Wakimoto modules, Proceedings of Symposia in Pure Mathematics, Volume: 92 (2016),1-16.
  7. (with A. Molev) Explicit generators in rectangular affine W-algebras of type A, arXiv:1403.1017 [math.RT].
  8. Rationality of W-algebras: principal nilpotent cases, Ann. Math. 182 (2015), 565-604.
  9. Rationality of admissible affine vertex algebras in the category O, Duke Math. J, Volume 165, Number 1 (2016), 67-93.
  10. Two-sided BGG resolutions of admissible representations, Represent. Theory 18 (2014), 183-222.
  11. (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.
  12. (with T. Kuwabara and F. Malikov) Localization of affine W-algebras, Comm. Math. Phys, April 2015, Volume 335, Issue 1, pp 143-182.
  13. W-algebras at the critical level, Contemp. Math., 565, 1--14, 2012.
  14. Rationality of Bershadsky-Polyakov vertex algebras, Comm. Math. Phys., October 2013, Volume 323, Issue 2, pp 627-633.
  15. Associated varieties of modules over Kac-Moody algebras and $C_2$-cofiniteness of W-algebras, Int. Math. Res. Notices (2015) Vol. 2015 11605--11666.
  16. A remark on the $C_2$-cofiniteness condition on vertex algebras, Math. Z. vol. 270, no. 1-2, 559-575, 2012.
  17. (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].
  18. (with P. Fiebig) The linkage principle for restricted critical level representations of affine Kac-Moody algebras, Compos. Math., 148, 1787--1810, 2012.
  19. (with F. Malikov) A chiral Borel-Weil-Bott theorem, Adv. Math., 229 (2012) 2908-2949.
  20. (with P. Fiebig) On the restricted Verma modules at the critical level, Trans. Amer. Math. Soc. 364 (2012), 4683-4712.
  21. (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.
  22. Representation theory of W-algebras, II, Adv. Stud. Pure Math. 61(2011), 51--90.
  23. Characters of representations of affine Kac-Moody Lie algebras at the critical level, arXiv:0706.1817v2 [math.QA].
  24. Representation Theory of W-Algebras, Invent. Math., Vol. 169 (2007), no. 2, 219--320.
  25. A New Proof of the Kac-Kazhdan Conjecture, Int. Math. Res. Not. 2006. Art. ID 27091, 5 pages.
  26. Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture, Duke Math. J., Vol. 130 (2005), No. 3, 435-478.
  27. Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction, Int. Math. Res. Not. 2004, no.15, 730--767.
  28. Drinfeld functor and finite-dimensional representations of Yangian, Comm. Math. Phys. 205 (1999), no. 1, 1--18.
  29. (with T. Suzuki) Duality between $sl_n(C)$ and the degenerate affine Hecke algebra, J. Algebra 209 (1998), no. 1, 288--304.
  30. (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.
  31. (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. 平成25年度代数学賞
  2. 平成20年度文部科学大臣表彰若手科学者賞
  3. 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