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： 2024年4月4日

研究室の紹介

いくつかの講演のビデオ

過去の講義

RIMS 表現論セミナー

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.

過去の研究集会

最近のプレプリント

  1. (with V. Futorny and L. Krizka) Generalized Grothendieck's simultaneous resolution and associated varieties of simple affine vertex algebras, arXiv:2404.02365[math.RT].
  2. (with X. Dai, J. Fasquel, Bohan Li and A. Moreau) On a series of simple affine VOAs at non-admissible level arising from rank one 4D SCFTs, arXiv:2403.04472 [math.RT].
  3. (with T. Creutzig and K. Kawasetsu) Weight representations of affine Kac-Moody algebras and small quantum groups, aarXiv:2311.10233[math.RT].
  4. (with T. Kuwabara and S. Möller) Hilbert Schemes of Points in the Plane and Quasi-Lisse Vertex Algebras with N=4 Symmetry, arXiv:2309.17308 [math.RT].
  5. (with L. Topley and J. J. Villarreal) The centre of the modular affine vertex algebra at the critical level, arXiv:2305.17765 [math.QA].
  6. (with J. van Ekeren and A. Moreau) Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras,arXiv:2102.13462 [math.RT].
  7. (with J. van Ekeren and A. Moreau) On the nilpotent orbits arising from admissible affine vertex algebras, arXiv:2010.08429 [math.RT], Proc. Lond. Math Soc., published online.
  8. (with T. Creutzig and B. Feigin) Urod algebras and Translation of W-algebras, arXiv:2010.02427 [math.RT], Forum of Mathematics, Sigma, Volume 10, 2022, e33.
  9. (with K. Kawasetsu and J. Sebag) A question of Joseph Ritt from the point of view of vertex algebras, arXiv:2009.04615 [math.QA], J. Algebra, Volume 588, 15 December 2021, Pages 118-128.
  10. (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.
  11. (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.
  12. (with J. van Ekeren) Rationality and Fusion Rules of Exceptional W-Algebras, arXiv:1905.11473 [math.RT], J. Eur. Math. Soc. (JEMS) (online first).
  13. Chiral algebras of class $\mathcal{S}$ and Moore-Tachikawa symplectic varieties, arXiv:1811.01577 [math.RT].

主要論文

  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 Theory, A 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.

全論文リストはこちら

解説論文及びレクチャーノート

  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.

賞罰

  1. 2022年JMSJ論文賞(with Hiromichi Yamada and Hiroshi Yamauchi)
  2. 平成31年度文部科学大臣表彰科学技術賞
  3. ICM2018招待講演
  4. 平成29年度日本数学会秋季賞
  5. 平成25年度代数学賞
  6. 平成20年度文部科学大臣表彰若手科学者賞
  7. 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