Proceedings of the Japan Academy, Series A, Mathematical Sciences

SVV algebras

Ruari Donald Walker

Full-text: Open access


In 2010 Shan, Varagnolo and Vasserot introduced a family of graded algebras in order to prove a conjecture of Kashiwara and Miemietz which stated that the finite-dimensional representations of affine Hecke algebras of type $D$ categorify a module over a certain quantum group. We study these algebras, and in various cases, show how they relate to Varagnolo-Vasserot algebras and to quiver Hecke algebras which in turn allows us to deduce various homological properties.

Article information

Proc. Japan Acad. Ser. A Math. Sci. Volume 94, Number 1 (2018), 7-12.

First available in Project Euclid: 5 January 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 16D90: Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality 17D99: None of the above, but in this section

SVV algebras Morita equivalence affine cellular affine quasi-hereditary


Walker, Ruari Donald. SVV algebras. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 1, 7--12. doi:10.3792/pjaa.94.7.

Export citation


  • J. Brundan, A. Kleshchev and P. J. McNamara, Homological properties of finite-type Khovanov-Lauda-Rouquier algebras, Duke Math. J. 163 (2014), no. 7, 1353–1404.
  • W. Cui, Affine cellularity of affine Birman-Murakami-Wenzl algebras, arXiv:1406.3516.
  • N. Enomoto and M. Kashiwara, Symmetric crystals and affine Hecke algebras of type B, Proc. Japan Acad. Ser. A Math. Sci. 82 (2006), no. 8, 131–136.
  • J. J. Graham and G. I. Lehrer, Cellular algebras, Invent. Math. 123 (1996), no. 1, 1–34.
  • M. Khovanov and A. D. Lauda, A diagrammatic approach to categorification of quantum groups. I, Represent. Theory 13 (2009), 309–347.
  • A. S. Kleshchev, Affine highest weight categories and affine quasihereditary algebras, Proc. Lond. Math. Soc. (3) 110 (2015), no. 4, 841–882.
  • A. S. Kleshchev, J. W. Loubert and V. Miemietz, Affine cellularity of Khovanov-Lauda-Rouquier algebras in type $A$, J. Lond. Math. Soc. (2) 88 (2013), no. 2, 338–358.
  • M. Kashiwara and V. Miemietz, Crystals and affine Hecke algebras of type D, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 7, 135–139.
  • S. Koenig and C. Xi, Affine cellular algebras, Adv. Math. 229 (2012), no. 1, 139–182.
  • R. Rouquier, 2-Kac-Moody algebras, arXiv:0812.5023v1.
  • P. Shan, M. Varagnolo and E. Vasserot, Canonical bases and affine Hecke algebras of type $D$, Adv. Math. 227 (2011), no. 1, 267–291.
  • M. Varagnolo and E. Vasserot, Canonical bases and affine Hecke algebras of type B, Invent. Math. 185 (2011), no. 3, 593–693.
  • R. D. Walker, On Morita equivalences between KLR algebras and VV algebras, arXiv:1603.00796.
  • G. Yang, Affine cellular algebras and Morita equivalences, Arch. Math. (Basel) 102 (2014), no. 4, 319–327.