Professor

Research Institute for Mathematical Sciences, Kyoto University

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

Research Interest: Representation Theory, Vertex Algebras

Last Update： 01-May-2018

RIMS Representation Theory Seminar

RIMS project 2018: Vertex operator algebras and symmetry

・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)

Papers

- (with A. Linshaw) Singular support of a vertex algebra and the arc space of its associated scheme, arXiv:1804.01287 [math.RT].
- (with A. Moreau) Arc spaces and chiral symplectic cores, arXiv:1802.06533 [math.RT].
- (with T. Creutzig and A. Linshaw) W-algebras as coset vertex algebras, arXiv:1801.03822 [math.QA].
- Representation theory of W-algebras and Higgs branch conjecture, submitted to the
*Proceedings of the ICM 2018.* - Associated Varieties and Higgs Branches (A Survey), to appear in
*Contemp. Math.* - (with C. Jiang) Coset Vertex Operator Algebras and W-Algebras,
*Sci. China Math.*61 (2018), no. 2, 191–206. 17B69. - (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.* - (with J. van Ekeren) Modularity of relatively rational vertex algebras and fusion rules of regular affine W-algebras, arXiv:1612.09100[math.RT].
- (with A. Premet) Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras
*, Trans. Moscow Math. Soc.***2017**, 217-234. - (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. - (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*.* - (with K. Kawasetsu) Quasi-lisse vertex algebras and modular linear differential equations, arXiv:1610.05865 [math.QA], to appear in
*Kostant Memorial Volume*, Birkhauser. - (with A. Moreau) On the irreducibility of associated varieties of W-algebras,
*J. Alg.*500, 15 April 2018, Pages 542-568. - (with V. Futorny, L.-E. Ramirez) Weight representations of admissible affine vertex algebras,
*Comm. Math. Phys*. 353 (2017), no.3, 1151-1178. - 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. - (with A. Moreau) Sheets and associated varieties of affine vertex algebras,
*Adv. Math,*Volume 320*,*7 November 2017, Pages 157–209. - (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. - (with A. Moreau) Joseph ideals and lisse minimal W-algebras,
*J. Inst. Math. Jussieu*, 17 (2018), no. 2, 397–417. - (with W. Wang) Modular affine vertex algebras and baby Wakimoto modules,
*Proc. Symp. Pure Math.,*Volume: 92 (2016)*,*14-29 - (with A. Molev) Explicit generators in rectangular affine W-algebras of type A,
*Lett. Math. Phys.*107(1), 47-59, 2017. - 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. - Two-sided BGG resolutions of admissible representations,
*Represent. Theory*18 (2014), 183-222. - (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. - (with T. Kuwabara and F. Malikov) Localization of affine W-algebras,
*Comm. Math. Phys,*April 2015, Volume 335, Issue 1, pp 143-182. - W-algebras at the critical level,
*Contemp. Math.,*565, 1--14, 2012. - Rationality of Bershadsky-Polyakov vertex algebras,
*Comm. Math. Phys.*, October 2013, Volume 323, Issue 2, pp 627-633. - 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 vertex algebra attached to the flag manifold and Lie algebra cohomology, AIP Conf. Proc. 1243, pp. 151-164, 2009, arXiv:0911.0922 [math.AG].
- (with P. Fiebig) The linkage principle for restricted critical level representations of affine Kac-Moody algebras,
*Compos. Math.,*148, 1787--1810, 2012. - (with F. Malikov) A chiral Borel-Weil-Bott theorem,
*Adv. Math.*, 229 (2012) 2908-2949. - (with P. Fiebig) On the restricted Verma modules at the critical level,
*Trans. Amer. Math. Soc.*364 (2012), 4683-4712. - (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, II,
*Adv. Stud. Pure Math.*61(2011), 51--90. - Characters of representations of affine Kac-Moody Lie algebras at the critical level, arXiv:0706.1817v2 [math.QA].
- Representation Theory of W-Algebras,
*Invent. Math.*, Vol. 169 (2007), no. 2, 219--320. - A New Proof of the Kac-Kazhdan Conjecture,
*Int. Math. Res. Not.*2006. Art. ID 27091, 5 pages. - Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture,
*Duke Math. J.*, Vol. 130 (2005), No. 3, 435-478. - Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction,
*Int. Math. Res. Not.*2004, no.15, 730--767. - Drinfeld functor and finite-dimensional representations of Yangian,
*Comm. Math. Phys.*205 (1999), no. 1, 1--18. - (with T. Suzuki) Duality between $sl_n(C)$ and the degenerate affine Hecke algebra,
*J. Algebra*209 (1998), no. 1, 288--304. - (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. - (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.

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