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:
2023年3月22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
- (with J. van Ekeren and A. Moreau) Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras,arXiv:2102.13462 [math.RT].
- (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.
- (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.
- (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.
- (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.
- (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.
- (with J. van Ekeren) Rationality and Fusion Rules of Exceptional W-Algebras, arXiv:1905.11473 [math.RT], J. Eur. Math. Soc. (JEMS) (online first).
- Chiral algebras of class $\mathcal{S}$ and Moore-Tachikawa symplectic varieties, arXiv:1811.01577 [math.RT].
主要論文
- (with E. Frenkel) Quantum Langlands duality of representations of W-algebras, Compos. Math. Volume 155, Issue 12, December 2019, 2235-2262.
- (with T. Creutzig and A. Linshaw) W-algebras as coset vertex algebras, Invent. Math., October 2019, Volume 218, Issue 1, pp 145–195.
- (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.
- (with A. Moreau) Joseph ideals and lisse minimal W-algebras, J. Inst. Math. Jussieu, 17 (2018), no. 2, 397–417.
- (with A. Premet) Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras, Trans. Moscow Math. Soc. 2017, 217-234.
- Rationality of W-algebras: principal nilpotent cases, Ann. Math. 182 (2015), 565-604.
- Rationality of admissible affine vertex algebras in the category O, Duke Math. J, Volume 165, Number 1 (2016), 67-93, errata.
- Associated varieties of modules over Kac-Moody algebras and $C_2$-cofiniteness of W-algebras, Int. Math. Res. Notices (2015) Vol. 2015 11605--11666.
- A remark on the $C_2$-cofiniteness condition on vertex algebras, Math. Z. vol. 270, no. 1-2, 559-575, 2012.
- (with F. Malikov) A chiral Borel-Weil-Bott theorem, Adv. Math., 229 (2012) 2908-2949.
- (with P. Fiebig) The linkage principle for restricted critical level representations of affine Kac-Moody algebras, Compos. Math., 148, 1787--1810, 2012.
- (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.
- Representation Theory of W-Algebras, Invent. Math., Vol. 169 (2007), no. 2, 219--320.
- Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture, Duke Math. J., Vol. 130 (2005), No. 3, 435-478.
- (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
- Representation theory of W-algebras and Higgs branch conjecture, Proc. Int. Cong. of Math. 2018 Rio de Janeiro, Vol. 1 (1261-1278).
- Associated Varieties and Higgs Branches (A Survey), Contemp. Math. 711(2018), 37-44.
- 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
- 2022年JMSJ論文賞(with Hiromichi Yamada and Hiroshi Yamauchi)
- 平成31年度文部科学大臣表彰科学技術賞
- ICM2018招待講演
- 平成29年度日本数学会秋季賞
- 平成25年度代数学賞
- 平成20年度文部科学大臣表彰若手科学者賞
- 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