arXiv subjects

I. N. Zurrián

Publications and source records attributed to I. N. Zurrián.

2 recordsLinked to original sources

arXiv2024

On the basic representation of the double affine Hecke algebra at critical level

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 studied by Oblomkov [O04] and further detailed by Gehles [G06] in the presence of minuscule weights.

math.RT↗

arXiv2016

Completeness of the Bethe Ansatz for an open $q$-boson system with integrable boundary interactions

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 that the Bethe Ansatz entails a complete basis of eigenfunctions for the commuting quantum integrals in terms of Macdonald's three-parameter hyperoctahedral Hall-Littlewood polynomials.

math-ph↗