Published papers

• P. Iliev, Gaudin model for the multinomial distribution, Ann. Henri Poincaré 25 (2024), no. 3, 1795--1810 (arXiv:2303.08206).
  
  
• P. Iliev, Higher-order heat equation and the Gelfand-Dickey hierarchy, Bull. Sci. Math. 191 (2024), Paper no. 103399, 39pp. (arXiv:2108.10857).
  
  
• N. Crampé, H. De Bie, P. Iliev and L. Vinet, Superspace realizations of the Bannai-Ito algebra, Lett. Math. Phys. 113 (2023), no. 5, article number 108 (arXiv:2306.02714).
  
  
• P. Iliev, Bivariate Bernstein-Szegő polynomials, Oberwolfach Report No. 43/2023, pp. 30--33, 2023.
  
  
• P. Iliev and Y. Xu, Hahn polynomials for hypergeometric distribution, Adv. in Appl. Math. 139 (2022), Paper No. 102364, 34pp. (arXiv:2012.12168).
  
  
• H. De Bie, P. Iliev, W. van de Vijver and L. Vinet, The Racah algebra: An overview and recent results, in "Lie Groups, Number Theory, and Vertex Algebras", pp. 3--20, Contemp. Math. 768, Amer. Math. Soc., Providence RI, 2021 (arXiv:2001.11195).
  
  
• P. Iliev and Y. Xu, Hahn polynomials on polyhedra and quantum integrability, Adv. Math. 364 (2020), 107032, 37pp. (arXiv:1707.03843).
  
  
• A. Delgado, L. Fernández and P. Iliev, Darboux transformations from the Appell-Lauricella operator, J. Math. Anal. Appl. 482 (2020), no. 2, 123546, 21pp. (arXiv:1909.07796).
  
  
• H. De Bie, P. Iliev and L. Vinet, Bargmann and Barut-Girardello models for the Racah algebra, J. Math. Phys. 60 (2019), no. 1, 011701, 13 pp. (arXiv:1811.04203).
  
  
• P. Iliev, Symmetry algebra for the generic superintegrable system on the sphere, J. High Energy Phys., 2018, no. 2, 44, front matter+22 pp. (arXiv:1712.06422).
  
  
• V. X. Genest, P. Iliev and L. Vinet, Coupling coefficients of su_q(1,1) and multivariate q-Racah polynomials, Nuclear Phys. B 927 (2018), 97--123 (arXiv:1702.04626).
  
  
• P. Iliev, The generic quantum superintegrable system on the sphere and Racah operators, Lett. Math. Phys. 107 (2017), no. 11, 2029--2045 (arXiv:1608.04590).
  
  
• G. Grantcharov, V. Grantcharov and P. Iliev, Solvable Lie algebras and graphs, J. Algebra 491 (2017), 474--489 (arXiv:1604.07856).
  
  
• P. Iliev and Y. Xu, Connection coefficients for classical orthogonal polynomials of several variables, Adv. Math. 310 (2017), 290--326 (arXiv:1506.04682).
  
  
• J. Geronimo and P. Iliev, Bernstein-Szegő measures, Banach algebras, and scattering theory, Trans. Amer. Math. Soc. 369 (2017), no. 8, 5581--5600 (arXiv:1408.0260).
  
  
• J. Geronimo, P. Iliev and W. Van Assche, Alpert multiwavelets and Legendre-Angelesco multiple orthogonal polynomials, SIAM J. Math. Anal. 49 (2017), no. 1, 626--645 (arXiv:1603.01986).
  
  
• J. Geronimo, P. Iliev and G. Knese, Polynomials with no zeros on a face of the bidisk, J. Funct. Anal. 270 (2016), no. 9, 3505--3558 (arXiv:1301.3510).
  
  
• J. Geronimo and P. Iliev, A hypergeometric basis for the Alpert multiresolution analysis, SIAM J. Math. Anal. 47 (2015), no. 1, 654--668 (arXiv:1403.0483).
  
  
• P. Iliev, Bispectral extensions of the Askey-Wilson polynomials, J. Funct. Anal. 266 (2014), no. 4, 2294--2318 (arXiv:1212.0137).
  
  
• J. Geronimo and P. Iliev, Fejér-Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle, J. Eur. Math. Soc. (JEMS) 16 (2014), no. 9, 1849--1880 (arXiv:1206.1526).
  
  
• P. Iliev, Krall-Laguerre commutative algebras of ordinary differential operators, Ann. Mat. Pura Appl. 192 (2013), no. 2, 203--224 (arXiv:1107.3773).
  
  
• P. Iliev, Meixner polynomials in several variables satisfying bispectral difference equations, Adv. in Appl. Math. 49 (2012), no. 1, 15--23 (arXiv:1112.5589).
  
  
• P. Iliev, A Lie-theoretic interpretation of multivariate hypergeometric polynomials, Compositio Math. 148 (2012), no. 3, 991--1002 (arXiv:1101.1683).
  
  
• J. Geronimo, P. Iliev and G. Knese, Orthogonality relations for bivariate Bernstein-Szegő measures, in "Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications", pp. 119--131, Contemp. Math. 578, Amer. Math. Soc., Providence RI, 2012 (arXiv:1111.5658).
  
  
• P. Iliev and P. Terwilliger, The Rahman polynomials and the Lie algebra , Trans. Amer. Math. Soc. 364 (2012), no. 8, 4225--4238 (arXiv:1006.5062).
  
  
• P. Iliev, Krall-Jacobi commutative algebras of partial differential operators, J. Math. Pures Appl. (9) 96 (2011), no. 5, 446--461 (arXiv:1011.2599).
  
  
• J. Geronimo and P. Iliev, Multivariable Askey-Wilson function and bispectrality, Ramanujan J. 24 (2011), no. 3, 273--287.
  
  
• P. Iliev, Bispectral commuting difference operators for multivariable Askey-Wilson polynomials, Trans. Amer. Math. Soc. 363 (2011), no. 3, 1577--1598 (arXiv:0801.4939).
  
  
• L. Haine, E. Horozov and P. Iliev, The trigonometric Grassmannian and a difference W-algebra, Transform. Groups 15 (2010), no. 1, 92--114.
  
  
• J. Geronimo and P. Iliev, Bispectrality of multivariable Racah-Wilson polynomials, Constr. Approx. 31 (2010), no. 3, 417--457 (arXiv:0705.1469).
  
  
• L. Haine, E. Horozov and P. Iliev, Trigonometric Darboux transformations and Calogero-Moser matrices, Glasg. Math. J. 51 (2009), issue A, 95--106 (arXiv:0807.2888).
  
  
• A. Delgado, J. Geronimo, P. Iliev and Y. Xu, On a two variable class of Bernstein-Szegő measures, Constr. Approx. 30 (2009), no. 1, 71--91 (arXiv:0710.0035).
  
  
• J. Geronimo and P. Iliev, Two variable deformations of the Chebyshev measure, in "Integrable Systems and Random Matrices: In Honor of Percy Deift", pp. 197--213, Contemp. Math. 458, Amer. Math. Soc., Providence RI, 2008 (arXiv:math/0612489).
  
  
• P. Iliev, Heat kernel expansions on the integers and the Toda lattice hierarchy, Selecta Math. (N.S.) 13 (2007), no. 3, 497--530 (arXiv:math-ph/0605079).
  
  
• P. Iliev, Rational Ruijsenaars-Schneider hierarchy and bispectral difference operators, Phys. D 229 (2007), no. 2, 184--190 (math-ph/0609011).
  
  
• P. Iliev and Y. Xu, Discrete orthogonal polynomials and difference equations of several variables, Adv. Math. 212 (2007), no. 1, 1--36 (math.CA/0508039).
  
  
• P. Iliev, Finite heat kernel expansions on the real line, Proc. Amer. Math. Soc. 135 (2007), no. 6, 1889--1894 (math-ph/0504046).
  
  
• A. Delgado, J. Geronimo, P. Iliev and F. Marcellán, Two variable orthogonal polynomials and structured matrices, SIAM J. Matr. Anal. Appl. 28 (2006), no. 1, 118--147.
  
  
• L. Haine and P. Iliev, Askey-Wilson type functions with bound states, Ramanujan J. 11 (2006), no. 3, 285--329 (math.QA/0203136).
  
  
• P. Iliev, On the heat kernel and the Korteweg-de Vries hierarchy, Ann. Inst. Fourier (Grenoble) 55 (2005), no. 6, 2117--2127, (math-ph/0504045).
  
  
• F. A. Grünbaum and P. Iliev, A noncommutative version of the bispectral problem, J. Comput. Appl. Math., 161 (2003), no. 1, 99--118.
  
  
• F. A. Grünbaum and P. Iliev, Heat kernel expansions on the integers, Math. Phys. Anal. Geom. 5 (2002),  no. 2, 183--200, (math.CA/0206089).
  
  
• L. Haine and P. Iliev, A rational analogue of the Krall polynomials, J. Phys. A, 34 (2001), no. 11, 2445--2457.
  
  
• L. Haine and P. Iliev, Commutative rings of difference operators and an adelic flag manifold, Internat. Math. Res. Notices 2000 (2000), no. 6, 281--323.
  
  
• P. Iliev, q-KP hierarchy, bispectrality and Calogero-Moser systems, J. Geom. Phys. 35 (2000), no. 2-3, 157--182.
  
  
• P. Iliev, Algèbres commutatives d'opérateurs aux q-différences et systèmes de Calogero-Moser, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 10, 877--882.
  
  
• P. Iliev, Solutions to Frenkel's deformation of the KP hierarchy, J. Phys. A 31 (1998), no. 12, L241--L244.
  
  
• P. Iliev, Tau function solutions to a q-deformation of the KP hierarchy, Lett. Math. Phys. 44 (1998), no. 3, 187--200.
  
  
• L. Haine and P. Iliev, The bispectral property of a q-deformation of the Schur polynomials and the q-KdV hierarchy, J. Phys. A 30 (1997), no. 20, 7217--7227.
  

Preprints:

• L. Fernández, J. Geronimo and P. Iliev, Compactly supported, orthogonal, continuous piecewise polynomial multiresolution analysis, arXiv:2412.02908.
  
  
• J. Geronimo and P. Iliev, Bernstein-Szegő measures in the plane, arXiv:2207.14383.
  
  
• W. R. Casper, E. Horozov, P. Iliev and M. Yakimov, A Burchnall-Chaundy-Krichever theory for fractional differential operators, arXiv:2108.12010.