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

Research Interest: Representation Theory, Vertex Algebras

Last Update： 24-May-2016

I will give a graduate course at MIT for Spring Semester, 2016. The details will be here.

RIMS Representation Theory Seminar

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

Papers

- (with V. Futorny, L.-E. Ramirez) Weight representations of admissible affine vertex algebras, arXiv:1605.07580 [math.RT].
- Introduction to W-algebras and their representation theory, arXiv:1605.00138 [math.RT].
- (with A. Moreau) Sheets and associated varieties of affine vertex algebras, arXiv:1601.05906 [math.RT].
- (with T. Creutzig and A. Linshaw) Cosets of Bershadsky-Polyakov algebras and rational $\mathcal{W}$-algebras of type $A$, arXiv:1511.09143 [math.RT].
- (with A. Moreau) Joseph ideals and lisse minimal W-algebras,
*J. Inst. Math. Jussieu*, published online. - (with W. Wang) Modular affine vertex algebras and baby Wakimoto modules, arXiv:1503.00395 [math.QA], to appear in
*the proceedings volume on the 2012-2014 Southeastern Lie Theory Workshops.* - (with A. Molev) Explicit generators in rectangular affine W-algebras of type A, arXiv:1403.1017 [math.RT].
- 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. - 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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