Jasper Stokman's home page
Jasper V. Stokman
Institute for Mathematics
Faculty of Science
Universiteit van Amsterdam
Science Park 105-107, 3rd floor (entrance via Nikhef)
1098 XG Amsterdam
1090 GE Amsterdam
Room number: F3.03
Telephone: +31 20 525 5202
Fax: +31 20 525 5101
j.v.stokman AT uva.nl.
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
and their interrelations.
Lie theory, in particular representation theory of
Lie groups, quantum groups and (double) affine Hecke algebras,
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,
I co-organise the symposium
From E6 to double affine E60 on the occasion of the 62nd birthday of Eric Opdam, which takes place in Amsterdam from August 31, 2022 until September 2, 2022.
WAYTA seminar in Representation Theory and Mathematical Physics
Graphical calculus for quantum vertex operators, I: The dynamical fusion operator,
arXiv:2205.09464. With Hadewijch De Clercq and Nicolai Reshetikhin.
Quasi-polynomial representations of double affine Hecke algebras,
arXiv:2204.13729. With Siddhartha Sahi and Vidya Venkateswaran.
Asymptotic boundary KZB operators and quantum Calogero-Moser spin chains, in ``Hypergeometry, Integrability and Lie Theory'', 205-241, Contemp. Math. 780, Amer. Math. Soc., Providence, RI, 2022. With Nicolai Reshetikhin.
N-point spherical functions and asymptotic boundary KZB equations, Invent. Math. 229 (2022), no. 1, 1-86. With Nicolai Reshetikhin.
- The skein category of the annulus, in: Representation Theory, Mathematical Physics, and Integrable Systems, 529-568, Progr. Math., 340, Birkhauser/Springer, Cham, 2021. With
Kayed Al Qasimi.
A nonsymmetric version of Okounkov's BC-type interpolation Macdonald polynomials, Transform. Groups 26 (2021), no. 4, 1261-1292.
With Niels Disveld and
Folded and contracted solutions of coupled classical dynamical Yang-Baxter and reflection equations, Indag. Math. (N.S.) 32 (2021), 1372-1411.
Some remarks on non-symmetric interpolation Macdonald polynomials, Int. Math. Res. Not. IMRN 2021, no. 19, 14814-14839. With
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.
Generalized Onsager algebras, Algebr. Represent. Theory 23
(2020), no. 4, 1523-1541.
Towers of solutions of qKZ equations and their applications to loop models,
Ann. Henri Poincaré 20 (2019), no. 11, 3743-3797, with Kayed Al Qasimi and Bernard Nienhuis.
- On connection matrices of quantum Knizhnik-Zamolodchikov equations based on Lie super algebras, in: "Representation Theory, Special Functions and Painleve
Equations - RIMS 2015", Adv. Studies in Pure Math. 76 (2018),
155-195, with Wellington Galleas.
- Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations, Adv. Math.
323 (2018), 486-528,
with Nicolai Reshetikhin
and Bart Vlaar.
- Boundary quantum Knizhnik-Zamolodchikov equations and fusion, Ann. Henri
Poincaré 17 (2016), no. 1, 137-177, with
Nicolai Reshetikhin and Bart Vlaar.
- Connection problems for quantum affine KZ equations and integrable lattice
models, Comm. Math. Phys. 338 (2015), no. 3, 1363-1409.
- Koornwinder polynomials and the XXZ spin chain, J. Approx. Theory
197 (2015), 69-100 (special issue dedicated to the 80th birthday
of Dick Askey), with Bart Vlaar.
- Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors,
Comm. Math. Phys. 336 (2015), no. 2, 953-986, with
Nicolai Reshetikhin and Bart Vlaar.
- Connection coefficients for basic Harish-Chandra series, Adv. Math.
250 (2014), 351-386.
- The c-function expansion of a basic hypergeometric function associated to
root systems, Ann. of Math. (2) 179 (2014), no. 1, 253-299.
General Overview of Multivariable Special Functions, in: "Multivariable Special Functions",
Second volume of the Encyclopedia of Special Functions: The Askey-Bateman Project (Series editors: M.E.H. Ismail, W. Van Assche; Volume editors: T.H. Koornwinder, J.V. Stokman), 1-18, Cambridge University Press (2021), with Tom Koornwinder (pdf).
Macdonald-Koornwinder polynomials, in: "Multivariable Special Functions",
Second volume of the Encyclopedia of Special Functions: The Askey-Bateman Project (Series editors: M.E.H. Ismail, W. Van Assche; Volume editors: T.H. Koornwinder, J.V. Stokman), 258-313, Cambridge University Press (2021) (pdf).
- Matching probabilities and loop models,
Amsterdam Science no. 3 (2016),14-15, with Bernard Nienhuis.
- Lecture notes on Koornwinder polynomials, Laredo Lectures on Orthogonal Polynomials and Special Functions, 145-207, Adv. Theory Spec. Funct. Orthogonal Polynomials, Nova Sci. Publ., Hauppauge, NY, 2004 (pdf).
PhD students and post-docs
- Hadewijch de Clercq (2019-present), jointly with Hendrik de Bie and Nicolai Reshetikhin.
- 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 Knizhnik-Zamolodchikov
- Fokko van de Bult, "Hyperbolic hypergeometric functions" (2007).
- Erdal Emsiz, "Affine Weyl Groups and Integrable
Systems with Delta-Potentials" (2006), jointly with Eric Opdam.