Zobrazeno 1 - 10
of 125
pro vyhledávání: '"van Diejen, J. F."'
Publikováno v:
Journal of Algebra and Its Applications, Vol. 23, No. 03, 2450061 (2024)
We construct the basic representation of the double affine Hecke algebra at critical level $q=1$ associated to an irreducible reduced affine root system $R$ with a reduced gradient root system. For $R$ of untwisted type such a representation was stud
Externí odkaz:
http://arxiv.org/abs/2412.09397
Autor:
van Diejen, J. F.
We show that the gradient flows associated with a recently found family of Morse functions converge exponentially to the roots of the symmetric continuous Hahn polynomials. By symmetry reduction the rate of the exponential convergence can be improved
Externí odkaz:
http://arxiv.org/abs/1911.05982
Autor:
van Diejen, J. F., Emsiz, E.
Publikováno v:
International Mathematics Research Notices 2019, No. 12, 3740--3767
We show that hyperoctahedral Whittaker functions---diagonalizing an open quantum Toda chain with one-sided boundary potentials of Morse type---satisfy a dual system of difference equations in the spectral variable. This extends a well-known bispectra
Externí odkaz:
http://arxiv.org/abs/1903.01827
Autor:
van Diejen, J. F., Emsiz, E.
Publikováno v:
Lett. Math. Phys. 109 (2019), no. 1, 89-112
Via the solutions of systems of algebraic equations of Bethe Ansatz type, we arrive at bounds for the zeros of orthogonal (basic) hypergeometric polynomials belonging to the Askey-Wilson, Wilson and continuous Hahn families.
Comment: 21 pages, L
Comment: 21 pages, L
Externí odkaz:
http://arxiv.org/abs/1903.00867
Autor:
van Diejen, J. F., Emsiz, E.
Publikováno v:
Math. Comp. 88 (2019), no. 317, 1229-1249
We employ a multivariate extension of the Gauss quadrature formula, originally due to Berens, Schmid and Xu [BSX95], so as to derive cubature rules for the integration of symmetric functions over hypercubes (or infinite limiting degenerations thereof
Externí odkaz:
http://arxiv.org/abs/1903.00868
Autor:
van Diejen, J. F., Emsiz, E.
Publikováno v:
Proc. Amer. Math. Soc. 146 (2018), no. 12, 5333-5347
We glue two families of Bernstein-Szego polynomials to construct the eigenbasis of an associated finite-dimensional Jacobi matrix. This gives rise to finite orthogonality relations for this composite eigenbasis of Bernstein-Szego polynomials. As an a
Externí odkaz:
http://arxiv.org/abs/1902.11062
Autor:
van Diejen, J. F., Emsiz, E.
Publikováno v:
Proc. Amer. Math. Soc. 146 (2018), no. 8, 3459-3472
We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For special choices of the parameters, this recovers the sixt
Externí odkaz:
http://arxiv.org/abs/1902.08506
Publikováno v:
Annales Henri Poincar\'e 19 (2018), 1349--1384
We employ a discrete integral-reflection representation of the double affine Hecke algebra of type $C^\vee C$ at the critical level q=1, to endow the open finite $q$-boson system with integrable boundary interactions at the lattice ends. It is shown
Externí odkaz:
http://arxiv.org/abs/1611.05922
Autor:
van Diejen, J. F., Emsiz, E.
Publikováno v:
Commun. Math. Phys. 350 (2017), no. 3, 1017--1067
We prove the orthogonality of the Bethe Ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove with repulsive homogeneous Robin boundary conditions at the walls. To this end these eigenfunctions are retrieved as the continuum limit
Externí odkaz:
http://arxiv.org/abs/1602.02152
Autor:
van Diejen, J. F., Emsiz, E.
Publikováno v:
Advanced Studies in Pure Mathematics 76 (2018), 125--153
Starting from a recently found branching formula for the six-parameter family of symmetric Macdonald-Koornwinder polynomials, we arrive by degeneration at corresponding branching rules for symmetric hypergeometric orthogonal polynomials of Wilson, co
Externí odkaz:
http://arxiv.org/abs/1601.06186