Maarten van Pruijssen

Mailing address:
Radboud Universiteit Nijmegen
Department of Mathematics
P.O. Box 9010
6500 GL Nijmegen
Visiting address:
Huygensgebouw
Heyendaalseweg 135
6525 AJ NIJMEGEN
email: m"dot"vanpruijssen"at"math"dot"ru"dot"nl
phone: --
office: HG03.709
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Welcome to my homepage. I am an assistant professor at the department of mathematics of the Radboud University in Nijmegen. My research interests include spherical varieties, representation theory of Lie groups, harmonic analysis, algebraic groups, branching rules, matrix-valued orthogonal polynomials.

Together with Erik Koelink, Stein Meereboer and Philip Schloesser, I am organizing a workshop in Nijmegen from 8 to 12 June 2026:

  • Quantum Symmetric Pairs, Hecke Algebras, and Representations: Exploring Spherical Functions (QSPHERE 2026).

    • Together with Wadim Zudilin and Erik Koelink, I have organized a conference in Nijmegen from 1 to 3 May 2024:

  • Hypergeometric and Orthogonal Polynomials Event (HOPE in May).

    • Together with Erik Koelink, I am advising the PhD students Philip Schloesser and Stein Meereboer, who are working on the project "Vector-valued Orthogonal Polynomials and Multiplicity Free Induction: Deformations and Quantizations" (NWO-M2, 2022-26).
    Together with Jasper Stokman, Mikhail Isachenkov and Erik Koelink, I have organized a seminar on Harmonic Analysis on Quantum Groups and Hecke Algebras (2022/23, 2023/24).
    May 6-9, 2024, I have taught a mini course on "Orthogonal polynomials and representation theory" in the Orthonet School in Logroño.

    Publications and preprints

    preprint

  • M. van Horssen and M. van Pruijssen, An elementary approach to non-symmetric shift operators and their q-analogs, 2026 (preprint).
  • M. van Horssen and M. van Pruijssen, Non-symmetric Jacobi polynomials of type BC1 as vector-valued polynomials Part 2: Shift operators, 2024 (preprint).
  • M. van Pruijssen, Vector-valued Heckman-Opdam polynomials: a Steinberg variation, 2023 (preprint).
  • M. van Pruijssen, The branching rules for SL(n+1,C),GL(n,C)) revisited: a spherical approach and applications to orthogonal polynomials, 2018 (preprint).

    • Publications

  • E. Depuydt and M. van Pruijssen, Multiplicity-free induction for the pairs (GL_2 × GL_2, diag(GL_2)) and (SL_3, GL_3) over finite fields, accepted for publication in J. Algebra Appl. (preprint)
  • M. van Pruijssen and P. Román, Matrix-valued classical pairs related to compact Gelfand pairs of rank one: families and shift operators, Results Math. 80 (2025), no. 7, Paper No. 211, 36 pp.
  • M. van Horssen and M. van Pruijssen, Non-symmetric Jacobi polynomials of type BC1 as vector-valued polynomials Part 1: spherical functions, Indag. Math. (N.S.) 36 (2025), no. 2, 593–608. (preprint).
  • M. van Pruijssen and G. Pezzini, On the extended weight monoid of a spherical homogeneous space and its applications to spherical functions, Represent. Theory 27(2023), 815–886. (preprint).
  • P. Crooks and M. van Pruijssen, An application of spherical geometry to hyperkähler slices, Canad. J. Math. 73(2021),no3,687 -- 716. (preprint).
  • E. Koelink and M. van Pruijssen and P. Román, Matrix elements of irreducible representations of SU(n+1) x SU(n+1) and matrix-valued orthogonal polynomials, Journal of Functional Analysis, 278(7), 2020, 108411. (preprint)
  • M. van Pruijssen, Spherical functions on spheres of rank two, Proceedings 50th Sophus Lie Seminar, Banach Center Publications, vol. 113. (Preprint).
  • M. van Pruijssen, Multiplicity free induced representations and orthogonal polynomials, IMRN 2017(doi: 10.1093/imrn/rnw295). (preprint)
  • M. van Pruijssen and P. Román, Matrix valued classical pairs related to compact Gelfand pairs of rank one, SIGMA 10 (2014), 113, 28 pages. (article).
  • G. Heckman and M. van Pruijssen, Matrix valued orthogonal polynomials for Gelfand pairs of rank one, Tohoku Math. J. (2) 68 (2016), no. 3, 407--437. (preprint).
  • E. Koelink and M. van Pruijssen and P. Román, Matrix valued orthogonal polynomials related to (SU(2)xSU(2), diag), II, Publ. RIMS Kyoto 49, no. 2, (2013), 271-312. (preprint).
  • E. Koelink and M. van Pruijssen and P. Román, Matrix valued orthogonal polynomials related to (SU(2)xSU(2), diag), International Mathematics Research Notices 2012, no. 24, 5673-5730. (preprint).

    • Software

    Together with Pablo Román I have written a GAP-code (Sp.g, SPn_lib.g) to calculate spherical functions on the compact Gelfand pair (Sp(2n),Sp(2n-2)xSp(2)). Feel free to improve and/or extend to other Gelfand pairs!

    The WHK/SHK-project: Representation theory, Computer Algebra and Special Functions that was kindly granted by the University of Paderborn resulted into two GAP-codes (PHI0.g, PHI0_library.g). These files came about with the help of my WHK (scientific assistant) Stanislav Smirnov. The results have been incorporated in the preprint Spherical functions on spheres of rank two. Here is a Mathematica notebook with a couple more calculations.

    Theses

  • Matrix valued orthogonal polynomials related to compact Gel'fand pairs of rank one, Ph.D.-thesis, 2012.
  • Tautological cycles on Jacobian varieties, master thesis, 2008.

    • Talks

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    Outreach

  • Frülings-Uni 2018, Workshop Die Schönheit von Seifenblasen für Oberstufen-Schülerinnen. Literatur: H. van Lint und J. Breeman, Zeepvliezen, Epsilon, 2004.
  • Herbst-Uni 2016, Vorlesung Graphen und Farben fÑŒr Oberstufen-Schülerinnen. Literatur: M. Aigner, G. Ziegler, Das Buch der Beweise, Springer 2010.

    • Teaching

    Nijmegen

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