On the semisimplicity of the cyclotomic quiver Hecke algebra of type $C$
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Abstract:
We provide criteria for the cyclotomic quiver Hecke algebras of type $C$ to be semisimple. In the semisimple case, we construct the irreducible modules.References
- Susumu Ariki and Euiyong Park, Representation type of finite quiver Hecke algebras of type $A^{(2)}_{2\ell }$, J. Algebra 397 (2014), 457–488. MR 3119233, DOI 10.1016/j.jalgebra.2013.09.005
- Susumu Ariki and Euiyong Park, Representation type of finite quiver Hecke algebras of type $D^{(2)}_{\ell +1}$, Trans. Amer. Math. Soc. 368 (2016), no. 5, 3211–3242. MR 3451875, DOI 10.1090/tran/6411
- Susumu Ariki and Euiyong Park, Representation type of finite quiver Hecke algebras of type $C^{(1)}_{\ell }$, Osaka J. Math. 53 (2016), no. 2, 463–489.
- Susumu Ariki, Euiyong Park, and Liron Speyer, Specht modules for quiver Hecke algebras of type $C$, arXiv:1703.06425, 2017, preprint.
- Jonathan Brundan and Alexander Kleshchev, Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras, Invent. Math. 178 (2009), no. 3, 451–484. MR 2551762, DOI 10.1007/s00222-009-0204-8
- Jonathan Brundan, Alexander Kleshchev, and Weiqiang Wang, Graded Specht modules, J. Reine Angew. Math. 655 (2011), 61–87. MR 2806105, DOI 10.1515/CRELLE.2011.033
- Matthew Fayers and Liron Speyer, Generalised column removal for graded homomorphisms between Specht modules, J. Algebraic Combin. 44 (2016), no. 2, 393–432. MR 3533560, DOI 10.1007/s10801-016-0674-x
- Victor G. Kac, Infinite-dimensional Lie algebras, 3rd ed., Cambridge University Press, Cambridge, 1990. MR 1104219, DOI 10.1017/CBO9780511626234
- Seok-Jin Kang and Masaki Kashiwara, Categorification of highest weight modules via Khovanov-Lauda-Rouquier algebras, Invent. Math. 190 (2012), no. 3, 699–742. MR 2995184, DOI 10.1007/s00222-012-0388-1
- Mikhail Khovanov and Aaron D. Lauda, A diagrammatic approach to categorification of quantum groups. I, Represent. Theory 13 (2009), 309–347. MR 2525917, DOI 10.1090/S1088-4165-09-00346-X
- Andrew Mathas, Cyclotomic quiver Hecke algebras of type $A$, Modular representation theory of finite and $p$-adic groups, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., vol. 30, World Sci. Publ., Hackensack, NJ, 2015, pp. 165–266. MR 3495747, DOI 10.1142/9789814651813_{0}005
- Raphaël Rouquier, $2$-Kac–Moody algebras, arXiv:0812.5023, 2008, preprint.
Additional Information
- Liron Speyer
- Affiliation: Department of Pure and Applied Mathematics, Osaka University, Suita, Osaka 565-0871, Japan
- Address at time of publication: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
- MR Author ID: 1076718
- Email: l.speyer@virginia.edu
- Received by editor(s): April 26, 2017
- Received by editor(s) in revised form: June 22, 2017
- Published electronically: December 4, 2017
- Communicated by: Kailash C. Misra
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1845-1857
- MSC (2010): Primary 20C08, 05E10, 16G10, 81R10
- DOI: https://doi.org/10.1090/proc/13876
- MathSciNet review: 3767340