Publications

Preprints

7	S.O. Warnaar and W. Zudilin q-Rious unimodality In memory of our mentor and friend Dick Askey.
6	S. Kanade, M.C. Russell, S. Tsuchioka and S.O. Warnaar Remarks on the conjectures of Capparelli, Meurman, Primc and Primc This paper provides representation-theoretic interpretations of the coloured partition identities of CMPP.
5	S.P. Albion, E.M. Rains and S.O. Warnaar Elliptic A_n Selberg integrals This paper gives elliptic analogues of the A_n Selberg and AFLT integrals. Constructive Approximation, to appear.
4	S.O. Warnaar An A₂ Bailey tree and A⁽¹⁾₂ Rogers–Ramanujan-type identities This paper gives a proof of the Kanade–Russell conjectures. Journal of the European Mathematical Society, to appear.
3	S.O. Warnaar The ₁ψ₁ summation Review on Ramanujan's ₁ψ₁ summation written for the Ramanujan Encyclopedia, to be published by Springer.
2	S.O. Warnaar Partial theta functions Review on partial theta functions written for the Ramanujan Encyclopedia, to be published by Springer.
1	S.O. Warnaar The A⁽²⁾_2n Rogers–Ramanujan identities Superseded by the Griffin–Ono–Warnaar paper.

Miscellany

6	S.O. Warnaar and W. Zudilin q-Rious and q-riouser Contribution to Dick Askey's Liber Amicorum, 2019.
5	S.O. Warnaar Symmetric functions , handwitten notes of the course on symmetric functons taught at Virginia Integrable Probability Summer School 2019. J. Lamers and S.O. Warnaar Exercises and detailed Solutions, including exercises on the Hopf algebra structure of Λ, plethystic notation, connections to representation theory, vertex operators and more.
4	H. Barcelo, B.L. Rothschild and S.O. Warnaar Fifty years of The Journal of Combinatorial Theory Journal of Combinatorial Theory A 144 (2016), 1–6.
3	T.H. Koornwinder, W. Van Assche and S.O. Warnaar A tribute to Dick Askey Journal of Approximation Theory 193 (2015), 1–3.
2	S.O. Warnaar and W. Zudilin The Riemann Hypothesis The Conversation, 7 December 2011. Part of a series of short popular articles on the Millennium Prize Problems.
1	S.O. Warnaar Hyp Australian Mathematical Society Gazette 29 (2002), 277–279. A short article on how to avoid rediscovering the Chu–Vandermonde sum more than 700 years after Chu Shih–Chieh.

Edited books and journal issues

5	M. Hallnäs, M. Noumi, V.P. Spiridonov and S.O. Warnaar, Editors Special issue on elliptic integrable systems, special functions and quantum field theory Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 16 (2020), 494 pages.
4	M.J. Schlosser, V.P. Spiridonov and S.O. Warnaar, Editors Special issue on elliptic hypergeometric functions and their applications Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 14 (2018), 517 pages.
3	M.E.H. Ismail, T.H. Koornwinder, P. Nevai, W. Van Assche and S.O. Warnaar, Editors Special issue dedicated to Dick Askey on the occasion of his 80th birthday Journal of Approximation Theory 197 (2015), 1–140.
2	M.E.H. Ismail, T.H. Koornwinder, P. Nevai, W. Van Assche and S.O. Warnaar, Editors Special issue dedicated to Dick Askey on the occasion of his 80th birthday Journal of Approximation Theory 195 (2015), 1–140.
1	J. de Gier and S.O. Warnaar, Editors Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics Journal of Physics: Conference Series 42 (2006), 299 pages.

Published Papers

80	S.O. Warnaar The A₂ Andrews–Gordon identities and cylindric partitions Transactions of the American Mathematical Society, Series B 10 (2023), 715–765.
79	S.P. Albion, E.M. Rains and S.O. Warnaar AFLT-type Selberg integrals Communications in Mathematical Physics 388 (2021), 735–791.
78	E.M. Rains and S.O. Warnaar Bounded Littlewood identities Memoirs of the American Mathematical Society, 270 (2021), No 1317, vii+115 pp.
77	C.-h Lee, , E.M. Rains and S.O. Warnaar An elliptic hypergeometric function approach to branching rules Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 16 (2020), 142, 52 pages.
76	H. Rosengren and S.O. Warnaar Elliptic hypergeometric functions associated with root systems Chapter 6 (pp. 159–186) of Encyclopedia of Special Functions, The Askey–Bateman Project, Volume II, Multivariable Special Functions Tom H. Koornwinder and Jasper V. Stokman, editors, Cambridge University Press, 2020.
75	A. Walsh and S.O. Warnaar Modular Nekrasov–Okounkov formulas Séminaire Lotharingien de Combinatoire 81 (2020), Art. B81c 28p.
74	E.M. Rains and S.O. Warnaar A Nekrasov–Okounkov formula for Macdonald polynomials Journal of Algebraic Combinatorics 48 (2018), 1–30.
73	R.P. Brent, C. Krattenthaler and S.O. Warnaar Discrete analogues of Macdonald–Mehta integrals Journal of Combinatorial Theory A 144 (2016), 80–138.
72	M.J. Griffin, K. Ono and S.O. Warnaar A framework of Rogers–Ramanujan identities and their arithmetic properties Duke Mathematical Journal 165 (2016), 1475–1527.
71	N. Bartlett and S.O. Warnaar Hall–Littlewood polynomials and characters of affine Lie algebras Advances in Mathematics 285 (2015), 1066–1105.
70	G. Károlyi, A. Lascoux and S.O. Warnaar Constant term identities and Poincaré polynomials Transactions of the American Mathematical Society 367 (2015), 6809–6836.
69	T. Chappell, A. Lascoux, S.O. Warnaar and W. Zudilin Logarithmic and complex constant term identities Computational and Analytical Mathematics, D.H. Bailey et al. (eds.), Springer Proceedings in Mathematics and Statistics, Volume 50, (2013), 219–250.
68	S.O. Warnaar Remarks on the paper "Skew Pieri rules for Hall–Littlewood functions" by Konvalinka and Lauve Journal of Algebraic Combinatorics 38 (2013), 519–526.
67	S.O. Warnaar Ramanujan’s ₁ψ₁ summation Notices of the AMS, 60, Number 1 (2013), 18–22. Alternatively, there is the full 7.5Mb article Srinivasa Ramanujan: Going strong at 125, Part II Notices of the AMS, 60, Number 1 (2013), 10–22.
66	S.O. Warnaar and W. Zudilin Dedekind’s eta-function and Rogers–Ramanujan identities Bulletin of the London Mathematical Society 44 (2012), 1–11.
65	V.P. Spiridonov and S.O. Warnaar New multiple ₆ψ₆ summation formulas and related conjectures The Ramanujan Journal 25 (2011), 319–342.
64	S.O. Warnaar and W. Zudilin A q-rious positivity Aequationes Mathematicae 81 (2011), 177–183.
63	A. Lascoux and S.O. Warnaar Branching rules for symmetric functions and sl_n basic hypergeometric series Advances in Applied Mathematics 46 (2011), 424–456.
62	S.O. Warnaar The sl₃ Selberg integral Advances in Mathematics 224 (2010), 499–524.
61	S.O. Warnaar A Selberg integral for the Lie algebra A_n Acta Mathematica 203 (2009), 269–304.
60	A. Lascoux, E.M. Rains and S.O. Warnaar Nonsymmetric interpolation Macdonald polynomials and gl_n basic hypergeometric series Transformation Groups 14 (2009), 613–647.
59	R. Langer, M.J. Schlosser and S.O. Warnaar Theta functions, elliptic hypergeometric series, and Kawanaka’s Macdonald polynomial conjecture Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5 (2009), 055, 20 pages.
58	S.O. Warnaar The Mukhin–Varchenko conjecture for type A 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings (2008).
57	P.J. Forrester and S.O. Warnaar The importance of the Selberg integral Bulletin of the American Mathematical Society (New Series) 45 (2008), 489–534.
56	S.O. Warnaar Bisymmetric functions, Macdonald polynomials and sl₃ basic hypergeometric series Compositio Mathematica 144 (2008), 271–303.
55	S.O. Warnaar On the generalised Selberg integral of Richards and Zheng Advances in Applied Mathematics 40 (2008), 212–218.
54	S.O. Warnaar Proof of the Flohr–Grabow–Koehn conjectures for characters of logarithmic conformal field theory Journal of Physics A: Mathematical and Theoretical 40 (2007), 12243–12254.
53	G.E. Andrews, and S.O. Warnaar The Bailey transform and false theta functions The Ramanujan Journal 14 (2007), 173–188.
52	G.E. Andrews and S.O. Warnaar The product of partial theta functions Advances in Applied Mathematics 39 (2007), 116–120.
51	J.-F. Fortin, P. Mathieu and S.O. Warnaar Characters of graded parafermion conformal field theory Advances in Theoretical and Mathematical Physics 11 (2007), 945–989.
50	V.P. Spiridonov and S.O. Warnaar Inversions of integral operators and elliptic beta integrals on root systems Advances in Mathematics 207 (2006), 91–132.
49	S.O. Warnaar Rogers–Szegő polynomials and Hall–Littlewood symmetric functions Journal of Algebra 303 (2006), 810–830.
48	S.O. Warnaar Hall–Littlewood functions and the A₂ Rogers–Ramanujan identities Advances in Mathematics 200 (2006), 403–434.
47	S.O. Warnaar q-Selberg integrals and Macdonald polynomials The Ramanujan Journal 10 (2005), 237–268.
46	S.O. Warnaar A generalization of the Farkas and Kra partition theorem for modulus 7 Journal of Combinatorial Theory A 110 (2005), 43–52.
45	S.O. Warnaar Summation formulae for elliptic hypergeometric series Proceedings of the American Mathematical Society 133 (2005), 519–527.
44	A. Berkovich and S.O. Warnaar Positivity preserving transformations for q-binomial coefficients Transactions of the American Mathematical Society 357 (2005), 2291–2351.
43	S.O. Warnaar q-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue’s identity and Euler’s pentagonal number theorem The Ramanujan Journal 8 (2004), 467–474.
42	S.O. Warnaar The Bailey lemma and Kostka polynomials Journal of Algebraic Combinatorics 20 (2004), 131–171.
41	S.O. Warnaar On the q-analogue of the sum of cubes Electronic Journal of Combinatorics 11 (2004), N13.
40	S.O. Warnaar Extensions of the well-poised and elliptic well-poised Bailey lemma Indagationes Mathematicae, New Series 14 (2003), 571–588.
39	S.O. Warnaar The generalized Borwein conjecture. II. Refined q-trinomial coefficients Discrete Mathematics 272 (2003), 215–258.
38	S.O. Warnaar Partial theta functions. I. Beyond the lost notebook Proceedings of the London Mathematical Society 87 (2003), 363–395.
37	S.O. Warnaar Partial-sum analogues of the Rogers–Ramanujan identities Journal of Combinatorial Theory A 99 (2002), 143–161.
36	S.O. Warnaar Summation and transformation formulas for elliptic hypergeometric series Constructive Approximation 18 (2002), 479–502.
35	A. Schilling and S.O. Warnaar Conjugate Bailey pairs. From configuration sums and fractional-level string functions to Bailey’s lemma Contemporary Mathematics 297 (2002), 227–255.
34	S.O. Warnaar The generalized Borwein conjecture. I. The Burge transform Contemporary Mathematics 291 (2001), 243–267.
33	S.O. Warnaar 50 Years of Bailey’s lemma in Algebraic Combinatorics and Applications, pp. 333–347, A. Betten et al. eds., (Springer, Berlin, 2001).
32	S.O. Warnaar Refined q-trinomial coefficients and character identities Journal of Statistical Physics 102 (2001), 1065–1081.
31	A. Schilling and S.O. Warnaar A generalization of the q-Saalschütz sum and the Burge transform in Physical Combinatorics, pp. 163–183, M. Kashiwara and T. Miwa eds., Progress in Mathematics 191, (Birkhäuser, Boston, 2000).
34	S.O. Warnaar Supernomial coefficients, Bailey’s lemma and Rogers–Ramanujan-type identities. A survey of results and open problems Séminaire Lotharingien de Combinatoire 42 (1999), Art. B42n 22p.
29	S.O. Warnaar q-Trinomial identities Journal of the Mathematical Physics 40 (1999), 2514–2530.
28	G.E. Andrews, A. Schilling, and S.O. Warnaar An A₂ Bailey lemma and Rogers–Ramanujan-type identities Journal of the American Mathematical Society 12 (1999), 677–702.
27	A. Schilling and S.O. Warnaar Inhomogeneous lattice paths, generalized Kostka polynomials and A_n-1 supernomials Communications in Mathematical Physics 202 (1999), 359–401.
26	A. Schilling and S.O. Warnaar Supernomial coefficients, polynomial identities and q-series The Ramanujan Journal 2 (1998), 459–494.
25	A. Schilling and S.O. Warnaar A higher level Bailey lemma: proof and application The Ramanujan Journal 2 (1998), 327–349.
24	S.O. Warnaar A note on the trinomial analogue of Bailey’s lemma Journal of Combinatorial Theory A 81 (1998), 114–118.
23	D.L. O’Brien, P.A. Pearce and S.O. Warnaar Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries Nuclear Physics B 501 [FS] (1997), 773–799.
22	A. Berkovich, B. M. McCoy, A. Schilling and S.O. Warnaar Bailey flows and Bose–Fermi identities for the conformal coset models (A₁⁽¹⁾)_N × (A₁⁽¹⁾)_N' / (A₁⁽¹⁾)_N+N' Nuclear Physics B 499 [PM] (1997), 621–649.
21	S.O. Warnaar The Andrews–Gordon identities and q-multinomial coefficients Communications in Mathematical Physics 184 (1997), 203–232.
20	A. Schilling and S.O. Warnaar A higher-level Bailey lemma International Journal of Modern Physics B 11 (1997), 189–195.
19	P.A. Pearce, D.L. O’Brien and S.O. Warnaar Finitized conformal spectrum of the Ising model on the cylinder and torus Physica A 228 (1996), 63–77.
18	S.O. Warnaar Fermionic solution of the Andrews–Baxter–Forrester model. II. Proof of Melzer’s polynomial identities Journal of Statistical Physics 84 (1996), 49–83.
17	S.O. Warnaar Fermionic solution of the Andrews–Baxter–Forrester model. I. Unification of CTM and TBA methods Journal of Statistical Physics 82 (1996), 657–685.
16	O. Foda, M. Okado and S.O. Warnaar A proof of polynomial identities of type sl(n)₁ ⊗ sl(n)₁ / sl(n)₂ Journal of Mathematical Physics 37 (1996), 965–986.
15	O. Foda, and S.O. Warnaar A bijection which implies Melzer’s polynomial identities: the χ _1,1^(p,p+1)case Letters in Mathematical Physics 36 (1996), 145–155.
14	S.O. Warnaar and P.A. Pearce A-D-E polynomial and Rogers–Ramanujan identities International Journal of Modern Physics A 11 (1996), 291–311.
13	U. Grimm and S.O. Warnaar Yang–Baxter algebras based on the two-colour BWM algebra Journal of Physics A 28 (1995), 7197–7207.
12	U. Grimm and S.O. Warnaar Solvable RSOS models based on the dilute BWM algebra Nuclear Physics B 435 [FS] (1995), 482–504.
11	S.O. Warnaar Algebraic construction of higher-rank dilute A models Nuclear Physics B 435 [FS] (1995), 463–481.
10	S.O. Warnaar and P.A. Pearce Exceptional structure of the dilute A₃ model: E₈ and E₇ Rogers–Ramanujan identities Journal of Physics A 27 (1994), L891–L897.
9	V.V. Bazhanov, B. Nienhuis and S.O. Warnaar Lattice Ising model in a field: E₈ scattering theory Physics Letters B 332 (1994), 198–206.
8	S.O. Warnaar, P.A. Pearce, B. Nienhuis and K.A. Seaton Order parameters of the dilute A models Journal of Statistical Physics 74 (1994), 469–531.
7	S.O. Warnaar, B. Nienhuis and K.A. Seaton A critical Ising model in a magnetic field International Journal of Modern Physics B7 (1993), 3727–3736.
6	S.O. Warnaar and B. Nienhuis Solvable lattice models labelled by Dynkin diagrams Journal of Physics A 26 (1993), 2301–2316.
5	B. Nienhuis, S.O. Warnaar and H.W.J. Blöte Exact multicritical behaviour of the Potts model Journal of Physics A 26 (1993), 477–493.
4	S.O. Warnaar, B. Nienhuis and K.A. Seaton New construction of solvable lattice models including an Ising model in a field Physical Review Letters 69 (1992), 710–712.
3	S.O. Warnaar A tri-tricritical Potts model Australian Mathematical Society Gazette 19 (1992), 51–57.
2	S.O. Warnaar, M.T. Batchelor and B. Nienhuis Critical properties of the Izergin–Korepin and solvable O(n) models and their related quantum spin chains Journal of Physics A 25 (1992), 3077–3095.
1	M.T. Batchelor, B. Nienhuis and S.O. Warnaar Bethe Ansatz results for a solvable O(n) model on the square lattice Physical Review Letters 62 (1989), 2425–2428.