Jasper Stokman's home page

Jasper V. Stokman
Korteweg-de Vries Institute for Mathematics
Faculty of Science
Universiteit van Amsterdam

Visiting address:
Science Park 105-107, 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
E-mail: 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

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.

First semester 2023-2024: local master course Automorphic Forms and Representation Theory with Mikhail Isachenkov.
Second semester 2023-2024: mastermath course Lie algebras with Eric Opdam.

Graphical calculus for quantum vertex operators, II: q-KZB and coordinate Macdonald-Ruijsenaars equations, arXiv:2411.17306. With Hadewijch De Clercq and Nicolai Reshetikhin.
Quasi-polynomial extensions of nonsymmetric Macdonald-Koornwinder polynomials, arXiv:2405.10609.
Quantum superintegrable spin systems on graph connections. Indag. Math. (N.S.), in press. Online version. With Nicolai Reshetikhin.
Quasi-polynomial representations of double affine Hecke algebras, arXiv:2204.13729. With Siddhartha Sahi and Vidya Venkateswaran.

2024.

Correction to: N-point spherical functions and asymptotic boundary KZB equations, Invent. Math. 237 (2024), 869-870.
Graphical calculus for quantum vertex operators, I: The dynamical fusion operator, Comm. Math. Phys. 405 (2024), Paper No. 149, 56 pp. With Hadewijch De Clercq and Nicolai Reshetikhin.

2022.

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.

2021.

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 Tom Koornwinder.
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 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, 1523-1541.

2019.

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.

2018.

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.

2016.

Boundary quantum Knizhnik-Zamolodchikov equations and fusion, Ann. Henri Poincaré 17 (2016), no. 1, 137-177, 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, 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.

2014.

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).