Jasper Stokman's home page
Coordinates
Jasper V. Stokman
Kortewegde Vries
Institute for Mathematics
Faculty of Science
Universiteit van Amsterdam
Visiting address:
Science Park 105107, 3rd floor (entrance via Nikhef)
1098 XG Amsterdam
The Netherlands
Postal address:
P.O.Box 94248
1090 GE Amsterdam
Room number: F3.03
Telephone: +31 20 525 5202
Email:
j.v.stokman AT uva.nl.
Research interests
I am professor in mathematics (chair Lie theory) at the
KdV Institute for Mathematics
(Universiteit van Amsterdam). I am a member
of the mathematical research cluster
Geometry and Quantum theory.
My research interests are

Lie theory, in particular representation theory of
Lie groups, quantum groups and (double) affine Hecke algebras,

Integrable systems,
in particular integrable quantum many body systems, integrable lattice models and conformal field theory,

Hypergeometric functions, in particular classical, basic and elliptic
hypergeometric functions associated to root systems,
and their interrelations.
Teaching
Preprints

Quasipolynomial extensions of nonsymmetric MacdonaldKoornwinder polynomials,
arXiv:2405.10609.

Quantum superintegrable spin systems on graph connections,
arXiv:2305.02767. With Nicolai Reshetikhin.
To appear in Indag. Math. (N.S.)

Graphical calculus for quantum vertex operators, I: The dynamical fusion operator,
arXiv:2205.09464. With Hadewijch De Clercq and Nicolai Reshetikhin. To appear in Comm. Math. Phys.

Quasipolynomial representations of double affine Hecke algebras,
arXiv:2204.13729. With Siddhartha Sahi and Vidya Venkateswaran.
Recent publications
2022.

Asymptotic boundary KZB operators and quantum CalogeroMoser spin chains, in ``Hypergeometry, Integrability and Lie Theory'', 205241, Contemp. Math. 780, Amer. Math. Soc., Providence, RI, 2022. With Nicolai Reshetikhin.

Npoint spherical functions and asymptotic boundary KZB equations, Invent. Math. 229 (2022), no. 1, 186. With Nicolai Reshetikhin.
2021.
 The skein category of the annulus, in: Representation Theory, Mathematical Physics, and Integrable Systems, 529568, Progr. Math., 340, Birkhauser/Springer, Cham, 2021. With
Kayed Al Qasimi.

A nonsymmetric version of Okounkov's BCtype interpolation Macdonald polynomials, Transform. Groups 26 (2021), no. 4, 12611292.
With Niels Disveld and
Tom Koornwinder.

Folded and contracted solutions of coupled classical dynamical YangBaxter and reflection equations, Indag. Math. (N.S.) 32 (2021), 13721411.

Some remarks on nonsymmetric interpolation Macdonald polynomials, Int. Math. Res. Not. IMRN 2021, no. 19, 1481414839. With
Siddhartha Sahi.

Metaplectic representations of Hecke algebras, Weyl group actions, and
associated polynomials, Selecta Math. (N.S.) 27 (2021), no. 3, Paper No. 47, 42pp. With Siddhartha Sahi and Vidya Venkateswaran.
2020.

Generalized Onsager algebras, Algebr. Represent. Theory 23
(2020), no. 4, 15231541.
2019.

Towers of solutions of qKZ equations and their applications to loop models,
Ann. Henri Poincaré 20 (2019), no. 11, 37433797, with Kayed Al Qasimi and Bernard Nienhuis.
2018.
 On connection matrices of quantum KnizhnikZamolodchikov equations based on Lie super algebras, in: "Representation Theory, Special Functions and Painleve
Equations  RIMS 2015", Adv. Studies in Pure Math. 76 (2018),
155195, with Wellington Galleas.
 Integral solutions to boundary quantum KnizhnikZamolodchikov equations, Adv. Math.
323 (2018), 486528,
with Nicolai Reshetikhin
and Bart Vlaar.
2016.
 Boundary quantum KnizhnikZamolodchikov equations and fusion, Ann. Henri
Poincaré 17 (2016), no. 1, 137177, with
Nicolai Reshetikhin and Bart Vlaar.
2015.
 Connection problems for quantum affine KZ equations and integrable lattice
models, Comm. Math. Phys. 338 (2015), no. 3, 13631409.
 Koornwinder polynomials and the XXZ spin chain, J. Approx. Theory
197 (2015), 69100 (special issue dedicated to the 80th birthday
of Dick Askey), with Bart Vlaar.
 Boundary quantum KnizhnikZamolodchikov equations and Bethe vectors,
Comm. Math. Phys. 336 (2015), no. 2, 953986, with
Nicolai Reshetikhin and Bart Vlaar.
2014.
 Connection coefficients for basic HarishChandra series, Adv. Math.
250 (2014), 351386.
 The cfunction expansion of a basic hypergeometric function associated to
root systems, Ann. of Math. (2) 179 (2014), no. 1, 253299.
Miscellaneous

General Overview of Multivariable Special Functions, in: "Multivariable Special Functions",
Second volume of the Encyclopedia of Special Functions: The AskeyBateman Project (Series editors: M.E.H. Ismail, W. Van Assche; Volume editors: T.H. Koornwinder, J.V. Stokman), 118, Cambridge University Press (2021), with Tom Koornwinder (pdf).

MacdonaldKoornwinder polynomials, in: "Multivariable Special Functions",
Second volume of the Encyclopedia of Special Functions: The AskeyBateman Project (Series editors: M.E.H. Ismail, W. Van Assche; Volume editors: T.H. Koornwinder, J.V. Stokman), 258313, Cambridge University Press (2021) (pdf).
 Matching probabilities and loop models,
Amsterdam Science no. 3 (2016),1415, with Bernard Nienhuis.
 Lecture notes on Koornwinder polynomials, Laredo Lectures on Orthogonal Polynomials and Special Functions, 145207, Adv. Theory Spec. Funct. Orthogonal Polynomials, Nova Sci. Publ., Hauppauge, NY, 2004 (pdf).
Editor
PhD students and postdocs
PhD students
 Hadewijch de Clercq, "Graphical calculus for quantum vertex operators" (2023).
 Kayed Al Qasimi, "An elevator ride with Knizhnik and Zamolodchikov" (2019), jointly with Bernard Nienhuis.
 Enno Diekema, "The fractional orthogonal derivative for functions of one and two variables" (2018). Main advisor: Tom Koornwinder.
 Michel van Meer, "Bispectral quantum KnizhnikZamolodchikov
equations" (2010).
 Fokko van de Bult, "Hyperbolic hypergeometric functions" (2007).
 Erdal Emsiz, "Affine Weyl Groups and Integrable
Systems with DeltaPotentials" (2006), jointly with Eric Opdam.
Postdocs