Iain Grant Gordon


  • Category O for cyclotomic rational Cherednik algebras (jt. with I.Losev), to appear in J. Eur. Math. Soc., arXiv:1109.2315v1 (pdf)
  • Monodromy of partial KZ functors for rational Cherednik algebras (jt. with M.Martino), in Symmetries, Integrable Systems and Representations, Springer Proceedings in Mathematics & Statistics, Vol. 40 (2013), 133-154. (pdf)
  • Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras (jt. with M.Chlouveraki and S.Griffeth), Contemp.Math. Vol 562 (2012), New Trends in Noncommutative Algebra, 77-89. (pdf)
  • Macdonald positivity via the Harish-Chandra D-module, Invent. Math. 187 (2012), no. 3, 637-643. (pdf)
  • Catalan numbers for complex reflection groups (jt with S.Griffeth), Amer. J. Math.134 (2012), no. 6, 1491-1502. (pdf)
  • Rational Cherednik Algebras, Proceedings of the International Congress of Mathematicians. Volume III, 1209-1225, Hindustan Book Agency, New Delhi, 2010. (pdf)
  • Haiman's work on the n! conjecture, and beyond Lectures at Grenoble Summer School on Representation Theory and Geometry, Séminaires et Congrès 24-I (2012), 199-225. (pdf)
  • Calogero-Moser space, restricted rational Cherednik algebras, and two-sided cells (jt with M.Martino), Math. Res. Lett. 16 (2009), no. 2, 255-262. (pdf)
  • Differential operators and Cherednik algebras, (jt. with V.Ginzburg and J.T.Stafford), Selecta Math. (N.S.) 14 (2009), no. 3-4, 629-666.(pdf)
  • Symplectic reflection algebras, Trends in Representation Theory of Algebras and Related Topics 2008. (pdf)
  • Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras, Int Math Res Papers (2008) Vol. 2008, 69 pages, doi:10.1093/imrp/rpn006 (pdf)
  • Cherednik, Hecke and quantum algebras as free Frobenius and Calabi-Yau extensions (jt with K.A.Brown and C.H.Stroppel),J.Algebra 319 (2008), 1007-1034. (pdf)
  • A remark on rational Cherednik algebras and differential operators on the cyclic quiver, Glasg. Math. J. 48 (2006), no. 1, 145--160. (pdf)
  • Rational Cherednik algebras and Hilbert schemes II: representations and sheaves (jt. with J.T.Stafford) Duke Math. J. 132 (2006), no. 1, 73--135 (pdf)
  • Rational Cherednik algebras and Hilbert schemes (jt. with J.T. Stafford), Adv. Math. 198 (2005), no. 1, 222--274. (pdf)
  • Representations of symplectic reflection algebras and resolutions of deformations of symplectic quotient singularities, (jt. with P. Smith) Mathematische Annalen 330 (2004), 185–200. (pdf)
  • Subregular representations of sl_n and simple singularities of type A_{n-1}. II, (jt. with D.Rumynin). Represent. Theory 8 (2004), 328-345. (pdf)
  • Subregular representations of sl_n and simple singularities of type A_{n-1}, (jt with D.Rumynin), Compositio Mathematica 138 (2003) 337-360. (pdf)
  • On the quotient ring by diagonal invariants, Invent. Math. 153 (2003), 503-518. (pdf)
  • Baby Verma modules for rational Cherednik algebras, Bull. London Math. Soc. 35 (2003) 321-336. (pdf)
  • Poisson orders, symplectic reflection algebras and representation theory, (jt. with K.A.Brown), J. reine angew. Math. 559 (2003), 193-216.  (pdf)
  • Block representation type of reduced enveloping algebras, (jt. with A.Premet), Trans. Amer. Math. Soc. 354 (2002), no. 4,1549--158. (pdf)
  • Representations of Lie algebras in positive characteristic and quantised enveloping algebras at roots of unity, in Quantum Groups and Lie Theory, London Mathematical Society Lecture Notes Series, 280. (pdf)
  • The ramification of the centres: quantised function algebras at roots of unity, (jt. with K.A.Brown), Proc.L.M.S. 84 (2002), 147-178. (pdf)
  • The ramification of the centres: Lie algebras in positive characteristic and quantised enveloping algebras, (jt.with K.A.Brown), Math.Zeit.238 (2001), 733-779. (pdf)
  • Complexity of representations of quantised function algebras and representation type,  J.Algebra 233 (2000), 437-482. (pdf)
  • Cohomology of quantized function algebras at roots of unity, Proc.L.M.S. 80 (2000), 337-359. (pdf)
  • Quantised function algebras at roots of unity and path algebras, J.Algebra 220 (1999), 381-395. (pdf)


  • The Auslander-Gorenstein property for Z-algebras , (jt. with J.T.Stafford), arXiv:1302.6640, (pdf)  
  • O_e(G) is a free module over O(G), (jt. with K.A.Brown and J.T.Stafford).  (pdf)  

Incomplete Preprints

  • The real loci of Calogero-Moser spaces, representations of rational Cherednik algebras and the Shapiro conjecture (jt with E.Horozov and M.Yakimov). (pdf)
    There is a gap in the proof of Theorem 3.2, so this paper does not (yet) re-prove the Shapiro-Shapiro conjecture. The error is on p.11: the sentence "But this last algebra is semisimple..." is not correct. These algebras are semisimple generically, but there is a ramification locus over which they are not. This locus needs to be understood better. To my mind, the main content of the paper (due to Horozov and Yakimov) is the connection between reality problems in geometry and reality problems in quiver-style representation theory. This is correct, and is clearly the original inspiration for more recent works on connections between Calogero-Moser spaces and Gaudin systems.
  • The Gelfand-Kirillov conjecture for symplectic reflection algebras. (pdf)
    To my chagrin, Yuri Berest and Oleg Chalykh discovered the generators and relations given in 2.4 are not correct. Specifically the commutation relation (3) needs to be changed. I do not know how to do this in general, and so the preprint is incorrect. As Yuri and Oleg pointed out there is a partial fix for functions on curves. Corollary 6.3 is correct, however, and is used in a paper by Brown-Changtong.

PhD Thesis

  • Representation theory of quantised function algebras at roots of unity (dvi).



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