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Jan Felipe van Diejen
Address:
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Email1: diejenATinst-matXutalcaXnl (X=dot) Email2: vanXdiejenATgmailXcom Phone: +56712201533 |
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I am a professor at the Instituto de Matemáticas of the Universidad de Talca in Chile.
RESEARCH:
My research falls within the area of Integrable Systems. This is a branch of Mathematical Physics that studies Exactly Solvable Models and Solitons. I am particularly interested in one-dimensional (quantum) integrable particle systems like the Lieb-Liniger model, the Calogero-Moser-Sutherland system, and the Toda chain. Some of my main contributions deal with (relativistic) deformations of these particle systems like the Ruijsenaars-Schneider models, and their connections with the Macdonald polynomials and the Macdonald-Koornwinder polynomials.
PUBLICATIONS:
See Google Scholar (or MathSciNet and Zentralblatt) for a complete list.
[2024a] van Diejen, J. F.: A Pieri formula for the characters of complex simple Lie algebras. Transform. Groups 29(1) (2024), 47--75.
[2024b] van Diejen, J. F.; Emsiz, E.; Zurrián, I. N.: On the basic representation of the double affine Hecke algebra at critical level. J. Algebra Appl. 23(3) (2024) 2450061.
[2023a] van Diejen, J. F.: Spectral analysis of an open q-difference Toda chain with two-sided boundary interactions on the finite integer lattice. Journal of Spectral Theory 13 (2023), 1261--1280.
[2023b] van Diejen, J. F.; Görbe, T.: Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess–Zumino–Witten fusion rings. Selecta Math. 29 (2023), 80.
[2023c] van Diejen, J. F.: Spectrum and Orthogonality of the Bethe Ansatz for the Periodic q-Difference Toda Chain on Zm+1, Ann. Henri Poincaré 24 (2023), 1877--1895.
[2023d] van Diejen, J. F.: Genus Zero sû(n)m Wess-Zumino-Witten fusion rules via Macdonald Polynomials, Comm. Math. Phys. 397 (2023), 967--994.
[2022a] van Diejen, J. F.; Görbe, T.: Elliptic Ruijsenaars operators on bounded partitions. Internat. Math. Res. Notices IMRN 2022 (2022), no. 24, 19335--19353.
[2022b] van Diejen, J.F.; Görbe, T.: Elliptic Racah polynomials. Lett. Math. Phys. 112 (2022), 66.
[2022c] van Diejen, J. F.: Harmonic analysis of boxed hyperoctahedral Hall-Littlewood polynomials. J. Funct. Anal. 282 (2022), 109256.
[2022d] van Diejen, J. F.; Görbe, T.: Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry. Comm. Math. Phys. (2022), 279--305.
[2022e] van Diejen, J. F.; Görbe, T.: Elliptic Kac-Sylvester matrix from difference Lamé equation. Ann. Henri Poincaré 23 (2022), 49--65.
[2021a] van Diejen, J. F.; Emsiz, E.; Zurrián, I. N.: Affine Pieri rule for periodic Macdonald spherical functions and fusion rings. Adv. Math. 392 (2021), 108027.
[2021b] van Diejen, J. F.; Emsiz, E.: Cubature rules for unitary Jacobi ensembles, Constructive Approx. 54 (2021), 145—156.
[2021c] van Diejen, J. F.; Emsiz, E.: Cubature rules from Hall-Littlewood polynomials. IMA Journal of Numerical Analysis 41 (2021), 998—1030.
[2021d] van Diejen, J.F.: q-deformation of the Kac-Sylvester tridiagonal matrix. Proc. Amer. Math. Soc. 149 (2021), no. 6, 2291—2304.
[2020a] van Diejen, J. F.: Deformation of Wess–Zumino–Witten fusion rules from open q-boson models with diagonal boundary conditions. J. Phys. A: Math. Theor. 53 (2020), 274002.
[2020b] van Diejen, J. F.: On the eigenfunctions of hyperbolic quantum Calogero–Moser–Sutherland systems in a Morse potential. Lett. Math. Phys. 110 (2020), 1215-1235.
[2020c] van Diejen, J. F.; Emsiz, E.: Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions. J. Differential Eqs. 268 (2020), no.8, 4525-4543.
[2019a] van Diejen, J. F.: Gradient system for the roots of the Askey-Wilson polynomial. Proc. Amer. Math. Soc. 147 (2019), no. 12, 5239—5249.
[2019b] van Diejen, J. F.; Emsiz, E.: Bispectral Dual Difference Equations for the Quantum Toda Chain with Boundary Perturbations. Internat. Math. Res. Notices IMRN 2019 (2019), no. 12, 3740—3767.
[2019c] van Diejen, J. F.; Emsiz, E.: Exact cubature rules for symmetric functions. Mathematics of Computation 88 (2019), no. 317, 1229—1249.
[2019d] van Diejen, J. F.; Emsiz, E.: Solutions of convex Bethe Ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials. Lett. Math. Phys. 109 (2019), 89—112.
[2018a] van Diejen, J. F.; Emsiz, E.: Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials. Proc. Amer. Math. Soc. 146 (2018), no. 12, 5333—5347.
[2018b] van Diejen, J. F.; Emsiz, E.; Zurrián, I. N.: Completeness of the Bethe Ansatz for an open q-boson system with integrable boundary interactions. Ann. Henri Poincaré 19 (2018), no. 5, 1349–1384.
[2018c] van Diejen, J. F.; Emsiz, E.: Branching rules for symmetric hypergeometric polynomials. Adv. Stud. Pure Math. 74 (2018), 125–153.
[2018d] van Diejen, J. F.; Emsiz, E.: Discrete Fourier transform associated with generalized Schur polynomials. Proc. Amer. Math. Soc. 146 (2018), no. 8, 3459–3472.
[2017] van Diejen, J. F.; Emsiz, E.: Orthogonality of Bethe ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove. Comm. Math. Phys. 350 (2017), no. 3, 1017–1067.
[2016] van Diejen, J. F.; Emsiz, E.: Spectrum and eigenfunctions of the lattice hyperbolic Ruijsenaars-Schneider system with exponential Morse term. Ann. Henri Poincaré 17 (2016), no. 7, 1615–1629.
[2015a] van Diejen, J. F.; Emsiz, E.: Branching formula for Macdonald-Koornwinder polynomials. J. Algebra 444 (2015), 606–614.
[2015b] van Diejen, J. F.; Emsiz, E.: Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit. Adv. Math. 285 (2015), 1225–1240.
[2015c] van Diejen, J. F.; Emsiz, E.: Integrable boundary interactions for Ruijsenaars' difference Toda chain. Comm. Math. Phys. 337 (2015), no. 1, 171–189.
[2014a] van Diejen, J. F.; Emsiz, E.: The semi-infinite q-boson system with boundary interaction. Lett. Math. Phys. 104 (2014), no. 1, 103–113.
[2014b] van Diejen, J. F.; Emsiz, E.: Orthogonality of Macdonald polynomials with unitary parameters. Math. Z. 276 (2014), no. 1-2, 517–542.
[2014c] van Diejen, J. F.; Emsiz, E.: Diagonalization of the infinite q-boson system. J. Funct. Anal. 266 (2014), no. 9, 5801–5817.
[2013] van Diejen, J. F.; Emsiz, E.: Discrete harmonic analysis on a Weyl alcove. J. Funct. Anal. 265 (2013), no. 9, 1981–2038.
[2012a] van Diejen, J. F.; Emsiz, E.: A discrete Fourier transform associated with the affine Hecke algebra. Adv. in Appl. Math. 49 (2012), no. 1, 24–38.
[2012b] van Diejen, J. F.; Emsiz, E. Unitary representations of affine Hecke algebras related to Macdonald spherical functions.: J. Algebra 354 (2012), 180–210.
[2011a] van Diejen, J. F.; Emsiz, E.: Pieri formulas for Macdonald's spherical functions and polynomials. Math. Z. 269 (2011), no. 1-2, 281–292.
[2011b] van Diejen, J. F.; Emsiz, E.: A generalized Macdonald operator. Int. Math. Res. Not. IMRN 2011, no. 15, 3560–3574.
[2008a] van Diejen, J. F.; Ito, M.: Difference Equations and Pieri Formulas for G 2 Type Macdonald Polynomials and Integrability. Lett. Math. Phys. 109 (2019), 89—112.
[2008b] Bustamante, M.D.; van Diejen, J. F.; de la Maza, A.C.: Norm formulae for the Bethe ansatz on root systems of small rank. J. Phys. A: Math. Theor. 41 (2008), 025202.
[2007a] van Diejen, J. F.; de la Maza, A.C.; Ryom-Hansen, S.: Bernstein-Szegö polynomials associated with root systems. Bull. London Math. Soc. 39 (2007), 837—847.
[2007b] van Diejen, J. F. Finite-dimensional orthogonality structures for Hall-Littlewood polynomials. Acta Appl. Math. 99 (2007), no. 3, 301–308.
[2007c] van Diejen, J. F.; Remarks on the zeros of the associated Legendre functions with integral degree. 99 (2007), no. 3, 293–299.
[2006] van Diejen, J. F. Diagonalization of an integrable discretization of the repulsive delta Bose gas on the circle. Comm. Math. Phys. 267 (2006), no. 2, 451–476.
[2005a] van Diejen, J. F.; Spiridonov, V. P. Unit circle elliptic beta integrals. Ramanujan J. 10 (2005), no. 2, 187–204.
[2005b] van Diejen, J. F.: Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber. Amer. J. Math. 127 (2005), no. 2, 421--458.
[2005c] van Diejen, J. F.: An asymptotic formula for the Koornwinder polynomials. J. Comput. Appl. Math. 178 (2005), no. 1-2, 465--471.
[2005d] van Diejen, J. F.: On the equilibrium configuration of the BC-type Ruijsenaars-Schneider system. J. Nonlinear Math. Phys. 12 (2005), suppl. 1, 689--696.
[2004a] van Diejen, J. F.: On the Plancherel formula for the (discrete) Laplacian in a Weyl chamber with repulsive boundary conditions at the walls. Ann. Henri Poincaré 5 (2004), no. 1, 135--168.
[2004b] van Diejen, J. F.; Lapointe, L.; Morse, J.: Determinantal construction of orthogonal polynomials associated with root systems. Compos. Math. 140 (2004), no. 2, 255--273.
[2003] van Diejen, J. F.: Asymptotic analysis of (partially) orthogonal polynomials associated with root systems. Int. Math. Res. Not. 2003 (2003), no. 7, 387--410.
[2002] van Diejen, J. F.; Spiridonov, V. P.: Elliptic beta integrals and modular hypergeometric sums: an overview. Rocky Mountain J. Math. 32 (2002), no. 2, 639--656.
[2001a] van Diejen, J. F.; Spiridonov, V. P.: Modular hypergeometric residue sums of elliptic Selberg integrals. Lett. Math. Phys. 58 (2001), no. 3, 223--238.
[2001b] van Diejen, J. F.; Spiridonov, V. P.: Elliptic Selberg integrals. Internat. Math. Res. Notices IMRN 2001 (2001), no. 20, 1083--1110.
[2001c] van Diejen, J. F.; Kirillov, A. N.: A remark on the Harish-Chandra series for hyperboloids. Physics and combinatorics 1999 (Nagoya), 11--15, World Sci. Publ., River Edge, NJ, 2001.
[2001d] van Diejen, J. F.; Kirillov, A. N.: Determinantal formulas for zonal spherical functions on hyperboloids. Math. Ann. 319 (2001), no. 2, 215--234.
[2000a] van Diejen, J. F.: Differential equations for multivariable Hermite and Laguerre polynomials. Calogero-Moser-Sutherland models (Montréal, QC, 1997), 145--159, CRM Ser. Math. Phys., Springer, New York, 2000.
[2000b] van Diejen, J. F.; Spiridonov, V. P.: An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums. Math. Res. Lett. 7 (2000), no. 5-6, 729--746.
[2000c] van Diejen, J. F.; Kirillov, A. N.: Formulas for q-spherical functions using inverse scattering theory of reflectionless Jacobi operators. Comm. Math. Phys. 210 (2000), no. 2, 335--369.
[2000d] van Diejen, J. F.; Puschmann, H.: Reflectionless Schrödinger operators, the dynamics of zeros, and the solitonic Sato formula. Duke Math. J. 104 (2000), no. 2, 269--318.
[2000e] van Diejen, J. F.: The dynamics of zeros of the solitonic Baker-Akhiezer function for the Toda chain. Internat. Math. Res. Notices IMRN 2000 (2000), no. 5, 253--270.
[2000f] van Diejen, J. F.; Kirillov, A. N.: A combinatorial formula for the associated Legendre functions of integer degree. Adv. Math. 149 (2000), no. 1, 61--88.
[1999a] van Diejen, J. F.: On the zeros of the KdV soliton Baker-Akhiezer function. Regul. Chaotic Dyn. 4 (1999), no. 2, 103--111.
[1999b] van Diejen, J. F.; Stokman J. V.: q-Racah polynomials for BC type root systems. Algebraic methods and q-special functions (Montréal, QC, 1996), 109--118, CRM Proc. Lecture Notes, 22, Amer. Math. Soc., Providence, RI, 1999.
[1999c] van Diejen, J. F.: A Sato formula for reflectionless finite difference operators. J. Math. Phys. 40 (1999), no. 11, 5822--5834.
[1999d] van Diejen, J. F.: Properties of some families of hypergeometric orthogonal polynomials in several variables. Trans. Amer. Math. Soc. 351 (1999), no. 1, 233--270.
[1998a] van Diejen, J. F.; Stokman J. V.: Multivariable q-Racah polynomials. Duke Math. J. 91 (1998), no. 1, 89--136.
[1998b] van Diejen, J. F.; Vinet, L.: The quantum dynamics of the compactified trigonometric Ruijsenaars-Schneider model. Comm. Math. Phys. 197 (1998), no. 1, 33--74.
[1997a] van Diejen, J. F.: On certain multiple Bailey, Rogers and Dougall type summation formulas. Publ. Res. Inst. Math. Sci. 33 (1997), no. 3, 483--508.
[1997b] van Diejen, J. F.: Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement. Comm. Math. Phys. 188 (1997), no. 2, 467--497.
[1997c] van Diejen, J. F.: Applications of commuting difference operators to orthogonal polynomials in several variables. Lett. Math. Phys. 39 (1997), no. 4, 341--347.
[1996a] van Diejen, J. F.: The relativistic Calogero model in an external field. Proceedings of the IV Wigner Symposium (Guadalajara, 1995), 470--477, World Sci. Publ., River Edge, NJ, 1996.
[1996b] van Diejen, J. F.: On the diagonalization of difference Calogero-Sutherland systems. Symmetries and integrability of difference equations (Estérel, PQ, 1994), 79--89, CRM Proc. Lecture Notes, 9, Amer. Math. Soc., Providence, RI, 1996.
[1996c] van Diejen, J. F.: Self-dual Koornwinder-Macdonald polynomials. Invent. Math. 126 (1996), no. 2, 319--339.
[1996d] Calogero, F.; van Diejen, J. F.: Solvable quantum version of an integrable Hamiltonian system. J. Math. Phys. 37 (1996), no. 9, 4243--4251.
[1995a] Calogero, F.; van Diejen, J. F.: An exactly solvable Hamiltonian system: quantum version. Phys. Lett. A 205 (1995), no. 2-3, 143–148.
[1995b] van Diejen, J. F.: Multivariable continuous Hahn and Wilson polynomials related to integrable difference systems.J. Phys. A 28 (1995), no. 13, L369--L374.
[1995c] van Diejen, J. F.: Difference Calogero-Moser systems and finite Toda chains. J. Math. Phys. 36 (1995), no. 3, 1299--1323.
[1995d] van Diejen, J. F.: Commuting difference operators with polynomial eigenfunctions. Compositio Math. 95 (1995), no. 2, 183--233.
[1994a] van Diejen, J. F.: Deformations of Calogero-Moser systems and finite Toda chains. Theoret. and Math. Phys. 99 (1994), no. 2, 549--554
[1994b] van Diejen, J. F.: Integrability of difference Calogero-Moser systems. J. Math. Phys. 35 (1994), no. 6, 2983--3004.
[1991] van Diejen, J. F.; Tip, A. Scattering from generalized point interactions using selfadjoint extensions in Pontryagin spaces. J. Math. Phys. 32 (1991), no. 3, 630--641.