Professor Ole Warnaar
Chair and Professor of Pure Maths
School of Mathematics and Physics
+61 7 336 53487
Priestley Building (67), Room 756
Personal page
Professor Ole Warnaar's personal page
Teaching and learning
Professor Warnaar teaches 3rd year algebra and number theory.
Book Chapters
Rosengren, H. and Warnaar, S. O. (2020). Elliptic hypergeometric functions associated with root systems. Encyclopedia of special functions: the Askey-Bateman Project. (pp. 159-186) Cambridge, United Kingdom: Cambridge University Press. doi: 10.1017/9780511777165.007
Chappell, Tom, Lascoux, Alain, Warnaar, S. Ole and Zudilin, Wadim (2013). Logarithmic and complex constant term identities. Computational and analytical mathematics. (pp. 219-250) edited by David H. Bailey, Heinz H. Bauschke, Peter Borwein, Frank Garvan, Michel Théra, Jon D. Vanderwerff and Henry Wolkowicz. New York, United States: Springer. doi: 10.1007/978-1-4614-7621-4_11
Journal Articles
P. Albion, Seamus, M. Rains, Eric and Warnaar, S. Ole (2025). Elliptic An Selberg Integrals. Constructive Approximation. doi: 10.1007/s00365-025-09705-8
Warnaar, S. Ole (2023). The A2 Andrews–Gordon identities and cylindric partition. Transactions of the American Mathematical Society Series B, 10 (22), 715-765. doi: 10.1090/btran/147
Albion, Seamus P., Rains, Eric M. and Warnaar, S. Ole (2021). AFLT-type Selberg integrals. Communications in Mathematical Physics, 388 (2), 735-791. doi: 10.1007/s00220-021-04157-0
Rains, Eric M. and Warnaar, S. Ole (2021). Bounded Littlewood identities. Memoirs of the American Mathematical Society, 270 (1317), 1-115. doi: 10.1090/memo/1317
Lee, Chul-Hee, Rains, Eric M. and Warnaar, S. Ole (2020). An elliptic hypergeometric function approach to branching rules. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 16 142, 1-52. doi: 10.3842/SIGMA.2020.142
Rains, Eric M. and Warnaar, S. Ole (2017). A Nekrasov–Okounkov formula for Macdonald polynomials. Journal of Algebraic Combinatorics, 48 (1), 1-30. doi: 10.1007/s10801-017-0790-2
Barcelo, Helene, Rothschild, Bruce L. and Warnaar, S. Ole (2016). Fifty years of The Journal of Combinatorial Theory. Journal of Combinatorial Theory. Series A, 144 (3), 1-6. doi: 10.1016/j.jcta.2016.06.003
Brent, Richard P., Krattenthaler, Christian and Warnaar, Ole (2016). Discrete analogues of Macdonald-Mehta integrals. Journal of Combinatorial Theory. Series A, 144, 80-138. doi: 10.1016/j.jcta.2016.06.005
Griffin, Michael J., Ono, Ken and Warnaar, S. Ole (2016). A framework of Rogers-Ramanujan identities and their arithmetic properties. Duke Mathematical Journal, 165 (8), 1475-1527. doi: 10.1215/00127094-3449994
Bartlett, Nick and Warnaar, S. Ole (2015). Hall-Littlewood polynomials and characters of affine Lie algebras. Advances in Mathematics, 285, 1066-1105. doi: 10.1016/j.aim.2015.08.011
Károlyi, Gyula, Lascoux, Alain and Ole Warnaar, S. (2015). Constant term identities and Poincaré polynomials. Transactions of the American Mathematical Society, 367 (10), 6809-6836. doi: 10.1090/tran/6119
Koornwinder, Tom, Van Assche, Walter and Warnaar, Ole (2015). A tribute to Dick Askey. Journal of Approximation Theory, 193, 1-3. doi: 10.1016/j.jat.2015.03.001
Alladi, Krishnaswami, Ono, Ken, Soundararajan, K., Vaughan, R. C. and Warnaar, S. Ole (2013). Srinivasa Ramanujan: Going Strong at 125, Part II. Notices of the American Mathematical Society, 60 (01), 10-22. doi: 10.1090/noti926
Warnaar, S. Ole (2013). Remarks on the paper "Skew Pieri rules for Hall-Littlewood functions" by Konvalinka and Lauve. Journal of Algebraic Combinatorics, 38 (3), 519-526. doi: 10.1007/s10801-013-0423-3
Warnaar, S. Ole and Zudilin, Wadim (2012). Dedekind's eta-function and Rogers-Ramanujan identities. Bulletin of the London Mathematical Society, 44 (1), 1-11. doi: 10.1112/blms/bdr019
Spiridonov, Vyacheslav P. and Warnaar, S. Ole (2011). New multiple 6ψ6 summation formulas and related conjectures. The Ramanujan Journal, 25 (3), 319-342. doi: 10.1007/s11139-011-9310-5
Warnaar, S. Ole and Zudilin, W. (2011). A q-rious positivity. Aequationes Mathematicae, 81 (1-2), 177-183. doi: 10.1007/s00010-010-0055-9
Lascoux, Alain and Warnaar, S. Ole (2011). Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series. Advances in Applied Mathematics, 46 (1-4), 424-456. doi: 10.1016/j.aam.2010.01.012
Warnaar, S. Ole (2010). The sl(3) Selberg integral. Advances in Mathematics, 224 (2), 499-524. doi: 10.1016/j.aim.2009.11.011
Warnaar, S. Ole (2009). A Selberg integral for the Lie algebra An. Acta Mathematica, 203 (2), 269-304. doi: 10.1007/s11511-009-0043-x
Lascoux, Alain, Rains, Eric. M. and Warnaar, S. Ole (2009). Nonsymmetric interpolation Macdonald polynomials and gln basic hypergeometric series. Transformation Groups, 14 (3), 613-647. doi: 10.1007/s00031-009-9061-1
Forrester, P. J. and Warnaar, S. O. (2008). The importance of the Selberg integral. Bulletin (New Series) of the American Mathematical Society, 45 (4), 489-534. doi: 10.1090/S0273-0979-08-01221-4
Warnaar, S. O. (2008). Bisymmetric functions, Macdonald polynomials and sl3 basic hypergeometric series. Compositio Mathematica, 144 (02), 271-303. doi: 10.1112/S0010437X07003211
Warnaar, S. O. (2008). On the generalised Selberg integral of Richards and Zheng. Advances in Applied Mathematics, 40 (2), 212-218. doi: 10.1016/j.aam.2006.12.002
Fortin, J. F., Mathieu, P. and Warnaar, S. O. (2007). Characters of graded parafermion conformal field theory. Advances in Theoretical and Mathematical Physics, 11 (6), 945-989.
Warnaar, S. O. (2007). Proof of the Flohr-Grabow-Koehn conjectures for characters of logarithmic conformal field theory. Journal Of Physics A-Mathematical And Theoretical, 40 (40), 12243-12254. doi: 10.1088/1751-8113/40/40/015
Andrews, G. E. and Warnaar, S. O. (2007). The Bailey transform and false theta functions. Ramanujan Journal, 14 (1), 173-188. doi: 10.1007/s11139-006-9006-4
Andrews, G. E. and Warnaar, S. O. (2007). The product of partial theta functions. Advances in Applied Mathematics, 39 (1), 116-120. doi: 10.1016/j.aam.2005.12.003
Vyacheslav P., Spiridonov, S. and Warnaar, S. O. (2006). Inversions of integral operators and elliptic beta integrals on root systems. Advances in Mathematics, 207 (1), 91-132. doi: 10.1016/j.aim.2005.11.007
Warnaar, S. Ole (2006). Rogers-Szego polynomials and Hall-Littlewood symmetric functions. Journal of Algebra, 303 (2), 810-830. doi: 10.1016/j.jalgebra.2006.04.026
Warnaar, S. O. (2006). Hall–Littlewood functions and the A2 Rogers–Ramanujan identities. Advances in Mathematics, 200 (2), 403-434. doi: 10.1016/j.aim.2004.12.001
Warnaar, S. O. (2005). A generalization of the Farkas and Kra partition theorem for modulus 7. Journal of Combinatorial Theory Series A, 110 (1), 43-52. doi: 10.1016/j.jcta.2004.08.008
Warnaar, S. O. (2005). Summation formulae for elliptic hypergeometric series. Proceedings of the American Mathematical Society, 133 (2), 519-527. doi: 10.1090/S0002-9939-04-07558-6
Berkovich, A. and Warnaar, S. O. (2005). Positivity preserving transformations for q-binomial coefficients. Transactions of the American Mathematical Society, 357 (6), 2291-2351. doi: 10.1090/S0002-9947-04-03680-3
Warnaar, S. O. (2005). q-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem. Ramanujan Journal, 8 (4), 467-474. doi: 10.1007/s11139-005-0275-0
Warnaar, S. O. (2004). The Bailey Lemma and Kostka Polynomials. Journal of Algebraic Combinatorics, 20 (2), 131-171. doi: 10.1023/B:JACO.0000047280.16877.1f
Warnaar, S. Ole (2004). On the q-analogue of the sum of cubes. The Electronic Journal of Combinatorics, 11 (1), N13-1-N13-2.
Warnaar, S. O. (2003). Extensions of the well-poised and elliptic well-poised Bailey lemma. Indagationes Mathematicae, 14 (3-4), 571-588. doi: 10.1016/S0019-3577(03)90060-7
Warnaar, S. O. (2003). The generalized borwein conjecture. II. Refined q-trinomial coefficients. Discrete Mathematics, 272 (2-3), 215-258. doi: 10.1016/S0012-365X(03)00047-5
Warnaar, S. O. (2003). Partial Theta Functions. I. Beyond the Lost Notebook. Proceedings of the London Mathematical Society, 87 (2), 363-395. doi: 10.1112/S002461150201403X
Warnaar, S. O. (2002). Partial-sum analogues of the Rogers-Ramanujan identities. Journal of Combinatorial Theory, Series A, 99 (1), 143-161. doi: 10.1006/jcta.2002.3266
Warnaar, S. O. (2002). Hyp. Australian Mathematical Society Gazette, 29 (5), 277-279.
Warnaar, S. O. (2002). Summation and transformation formulas for elliptic hypergeometric series. Constructive Approximation, 18 (4), 479-502. doi: 10.1007/s00365-002-0501-6
Warnaar, SO (2001). Refined q-trinomial coefficients and character identities. Journal of Statistical Physics, 102 (3-4), 1065-1081. doi: 10.1023/A:1004827709169
Andrews, GE, Schilling, A and Warnaar, SO (1999). An A(2) Bailey lemma and Rogers-Ramanujan-type identities. Journal of the American Mathematical Society, 12 (3), 677-702. doi: 10.1090/S0894-0347-99-00297-0
Warnaar, SO (1999). q-trinomial identities. Journal of Mathematical Physics, 40 (5), 2514-2530. doi: 10.1063/1.532880
Schilling, A and Warnaar, SO (1999). Inhomogeneous lattice paths, generalized Kostka polynomials and A(n-1) supernomials. Communications in Mathematical Physics, 202 (2), 359-401. doi: 10.1007/s002200050586
Warnaar, SO (1998). A note on the trinomial analogue of Bailey's lemma. Journal of Combinatorial Theory Series a, 81 (1), 114-118. doi: 10.1006/jcta.1997.2830
Schilling, A and Warnaar, SO (1998). A higher level Bailey lemma: Proof and application. Ramanujan Journal, 2 (3), 327-349. doi: 10.1023/A:1009746932284
Schilling, A and Warnaar, SO (1998). Supernomial coefficients, polynomial identities and q-series. Ramanujan Journal, 2 (4), 459-494. doi: 10.1023/A:1009780810189
OBrien, DL, Pearce, PA and Warnaar, SO (1997). Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries. Nuclear Physics B, 501 (3), 773-799. doi: 10.1016/S0550-3213(97)00424-0
Berkovich, A, McCoy, BM, Schilling, A and Warnaar, SO (1997). Bailey flows and Bose-Fermi identities for the conformal coset models (A(1)((1)))(N) x (A(1)((1)))(N')/(A(1)((1)))(N+N'). Nuclear Physics B, 499 (3), 621-649. doi: 10.1016/S0550-3213(97)82955-0
Warnaar, SO (1997). The Andrews-Gordon identities and q-multinomial coefficients. Communications in Mathematical Physics, 184 (1), 203-232. doi: 10.1007/s002200050058
Warnaar, SO (1996). Fermionic solution of the Andrews-Baxter-Forrester model .2. Proof of Melzer's polynomial identities. Journal of Statistical Physics, 84 (1-2), 49-83. doi: 10.1007/BF02179577
OBrien, DL, Pearce, PA and Warnaar, SO (1996). Finitized conformal spectrum of the Ising model on the cylinder and torus. Physica a, 228 (1-4), 63-77. doi: 10.1016/S0378-4371(96)00055-6
Foda, O, Okado, M and Warnaar, SO (1996). A proof of polynomial identities of type s(l(n))over-cap(1)circle times s(l(n))over-cap(1)/s(l(n))over-cap(2). Journal of Mathematical Physics, 37 (2), 965-986. doi: 10.1063/1.531698
Foda, O and Warnaar, SO (1996). A bijection which implies Melzer's polynomial identities: The chi(1,1)((p,p+1)) case. Letters in Mathematical Physics, 36 (2), 145-155. doi: 10.1007/BF00714377
Grimm, U and Warnaar, SO (1995). Yang-Baxter algebras based on the two-colour BWM algebra. Journal of Physics A-Mathematical and General, 28 (24), 7197-7207. doi: 10.1088/0305-4470/28/24/017
GRIMM, U and WARNAAR, SO (1995). SOLVABLE RSOS MODELS BASED ON THE DILUTE BWM ALGEBRA. Nuclear Physics B, 435 (3), 482-504. doi: 10.1016/0550-3213(94)00405-4
WARNAAR, SO (1995). ALGEBRAIC CONSTRUCTION OF HIGHER-RANK DILUTE A-MODELS. Nuclear Physics B, 435 (3), 463-481. doi: 10.1016/0550-3213(94)00424-D
WARNAAR, SO and PEARCE, PA (1994). EXCEPTIONAL STRUCTURE OF THE DILUTE A(3) MODEL - E(8) AND E(7) ROGERS-RAMANUJAN IDENTITIES. Journal of Physics A-Mathematical and General, 27 (23), L891-L897. doi: 10.1088/0305-4470/27/23/005
BAZHANOV, VV, NIENHUIS, B and WARNAAR, SO (1994). LATTICE ISING-MODEL IN A FIELD - E8 SCATTERING-THEORY. Physics Letters B, 322 (3), 198-206. doi: 10.1016/0370-2693(94)91107-X
WARNAAR, SO, PEARCE, PA, SEATON, KA and NIENHUIS, B (1994). ORDER PARAMETERS OF THE DILUTE A-MODELS. Journal of Statistical Physics, 74 (3-4), 469-531. doi: 10.1007/BF02188569
WARNAAR, SO and NIENHUIS, B (1993). SOLVABLE LATTICE MODELS LABELED BY DYNKIN DIAGRAMS. Journal of Physics A-Mathematical and General, 26 (10), 2301-2316. doi: 10.1088/0305-4470/26/10/005
NIENHUIS, B, WARNAAR, SO and BLOTE, HWJ (1993). EXACT MULTICRITICAL BEHAVIOR OF THE POTTS-MODEL. Journal of Physics A-Mathematical and General, 26 (3), 477-493. doi: 10.1088/0305-4470/26/3/013
WARNAAR, SO, NIENHUIS, B and SEATON, KA (1992). NEW CONSTRUCTION OF SOLVABLE LATTICE MODELS INCLUDING AN ISING-MODEL IN A FIELD. Physical Review Letters, 69 (5), 710-712. doi: 10.1103/PhysRevLett.69.710
WARNAAR, SO, BATCHELOR, MT and NIENHUIS, B (1992). CRITICAL PROPERTIES OF THE IZERGIN-KOREPIN AND SOLVABLE O(N) MODELS AND THEIR RELATED QUANTUM SPIN CHAINS. Journal of Physics A-Mathematical and General, 25 (11), 3077-3095. doi: 10.1088/0305-4470/25/11/016
BATCHELOR, MT, NIENHUIS, B and WARNAAR, SO (1989). BETHE-ANSATZ RESULTS FOR A SOLVABLE O(N) MODEL ON THE SQUARE LATTICE. Physical Review Letters, 62 (21), 2425-2428. doi: 10.1103/PhysRevLett.62.2425
SCHILPEROORT, RA, VELDSTRA, H, WARNAAR, SO, MULDER, G and COHEN, JA (1967). FORMATION OF COMPLEXES BETWEEN DNA ISOLATED FROM TOBACCO CROWN GALL TUMOURS AND RNA COMPLEMENTARY TO AGROBACTERIUM TUMEFACIENS DNA. Biochimica Et Biophysica Acta, 145 (2), 523-+. doi: 10.1016/0005-2787(67)90075-5
WARNAAR, SO, KNEGT, E, CHARLES, R, SCHILPEROORT, RA and GROSE, WJ (1965). PREPARATION BY ALKALINE TREATMENT OF A SERUMBLOCKING ANTIGEN OF VACCINIA VIRUS WITH IMMUNIZING POTENCY. Archiv Fur Die Gesamte Virusforschung, 17 (5), 577-+. doi: 10.1007/BF01262234
Conference Papers
Langer, Robin, Schlosser, Michael J. and Warnaar, S. Ole (2009). Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture. Workshop on Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions, Bonn, Germany, 21-25 Jul 2008. Kyiv, Ukraine: Natsional'na Akademiya Nauk Ukrainy. doi: 10.3842/SIGMA.2009.055
Warnaar, S. Ole (2008). The Mukhin-Varchenko conjecture for type A. FPSAC 2008: 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics, Viña del Mar, Chile, 23-27 June, 2008. Nancy, France: INRIA.
Warnaar, S. O. (2005). q-Selberg Integrals and Macdonald Polynomials. Conference on Number Theory and Combinatorics in Physics, Gainesville, Florida, 21-23 Mar 2003. Dordrecht, The Netherlands: Springer. doi: 10.1007/s11139-005-4849-7
Schilling , A. and Warnaar, S. O. (2002). Conjugate Bailey pairs. From configuration sums and fractional-level string functions to Bailey's lemma. Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory, Charlottesville, Virginia, USA, 23 - 27 may 2000. American Mathematical Society.
Warnaar, SO (2001). 50 years of Bailey's lemma. Euroconference on Algebraic Combinatorics and Applications (Alcoma99), Grossweinstein Germany, Sep 12-19, 1999. BERLIN: SPRINGER-VERLAG BERLIN.
Schilling, A and Warnaar, SO (2000). A generalization of the q-Saalschutz sum and the Burge transform. Workshop on Physical Combinatorics, Kyoto Japan, Feb 01-02, 1999. CAMBRIDGE: BIRKHAUSER BOSTON.
Schilling, A and Warnaar, SO (1997). A higher-level Bailey lemma. Proceedings of the Conference on Exactly Soluble Models in Statistical Mechanics - Current Status and Historical Perspectives, Boston Ma, Mar, 1996. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. doi: 10.1142/S0217979297000253
WARNAAR, SO, NIENHUIS, B and SEATON, KA (1993). A CRITICAL ISING-MODEL IN A MAGNETIC-FIELD. Conf On Yang-Baxter Equations in Paris, Paris France, Jul 24-30, 1992. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. doi: 10.1142/S0217979293003474
Newspaper Article
Warnaar, Ole and Zudilin, Wadim (2011, 12 07). The Riemann Hypothesis